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An h $h$ -principle for embeddings transverse to a contact structure
接触结构横向嵌入的 h $h$ 原则
IF 1.1
2区 数学
Robert Cardona, Francisco Presas
{"title":"An \u0000 \u0000 h\u0000 $h$\u0000 -principle for embeddings transverse to a contact structure","authors":"Robert Cardona, Francisco Presas","doi":"10.1112/topo.12326","DOIUrl":"https://doi.org/10.1112/topo.12326","url":null,"abstract":"<p>Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general <math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principle. The flexibility follows from the <math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full <math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140104530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On fillings of contact links of quotient singularities
论商数奇点接触链路的填充
IF 1.1
2区 数学
Zhengyi Zhou
{"title":"On fillings of contact links of quotient singularities","authors":"Zhengyi Zhou","doi":"10.1112/topo.12329","DOIUrl":"https://doi.org/10.1112/topo.12329","url":null,"abstract":"<p>We study several aspects of fillings for links of general isolated quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on the non-existence of exact fillings of contact links of isolated terminal quotient singularities. We provide an extensive list of isolated terminal quotient singularities whose contact links are not exactly fillable, including <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Z</mi>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>${mathbb {C}}^n/({mathbb {Z}}/2)$</annotation>\u0000 </semantics></math> for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 3$</annotation>\u0000 </semantics></math>, which settles a conjecture of Eliashberg, quotient singularities from general cyclic group actions and finite subgroups of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SU(2)$</annotation>\u0000 </semantics></math>, and all terminal quotient singularities in complex dimension 3. We also obtain uniqueness of the <i>orbifold</i> diffeomorphism type of <i>exact orbifold fillings</i> of contact links of some isolated terminal quotient singularities.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140069661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A characterization of heaviness in terms of relative symplectic cohomology
用相对交映同调表征重度
IF 1.1
2区 数学
Cheuk Yu Mak, Yuhan Sun, Umut Varolgunes
{"title":"A characterization of heaviness in terms of relative symplectic cohomology","authors":"Cheuk Yu Mak, Yuhan Sun, Umut Varolgunes","doi":"10.1112/topo.12327","DOIUrl":"https://doi.org/10.1112/topo.12327","url":null,"abstract":"<p>For a compact subset <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> of a closed symplectic manifold <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M, omega)$</annotation>\u0000 </semantics></math>, we prove that <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140069758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
奇维流形差分同调的一些理性同调计算
IF 1.1
2区 数学
Johannes Ebert, Jens Reinhold
{"title":"Some rational homology computations for diffeomorphisms of odd-dimensional manifolds","authors":"Johannes Ebert, Jens Reinhold","doi":"10.1112/topo.12324","DOIUrl":"https://doi.org/10.1112/topo.12324","url":null,"abstract":"<p>We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>U</mi>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>n</mi>\u0000 </msubsup>\u0000 <mo>:</mo>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mo>#</mo>\u0000 <mi>g</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∖</mo>\u0000 <mi>int</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$U_{g,1}^n:= #^g(S^n times S^{n+1})setminus mathrm{int}(D^{2n+1})$</annotation>\u0000 </semantics></math>, for large <math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, up to degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n-3$</annotation>\u0000 </semantics></math>. The answer is that it is a free graded commutative algebra on an appropriate set of Miller–Morita–Mumford classes. Our proof goes through the classical three-step procedure: (a) compute the cohomology of the homotopy automorphisms, (b) use surgery to compare this to block diffeomorphisms, and (c) use pseudoisotopy theory and algebraic <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 ","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12324","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139655252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Iteration of Cox rings of klt singularities
klt 奇点考克斯环的迭代
IF 1.1
2区 数学
Lukas Braun, Joaquín Moraga
{"title":"Iteration of Cox rings of klt singularities","authors":"Lukas Braun, Joaquín Moraga","doi":"10.1112/topo.12321","DOIUrl":"https://doi.org/10.1112/topo.12321","url":null,"abstract":"<p>In this article, we study the iteration of Cox rings of klt singularities (and Fano varieties) from a topological perspective. Given a klt singularity <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Δ</mi>\u0000 <mo>;</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,Delta;x)$</annotation>\u0000 </semantics></math>, we define the iteration of Cox rings of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Δ</mi>\u0000 <mo>;</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,Delta;x)$</annotation>\u0000 </semantics></math>. The first result of this article is that the iteration of Cox rings <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>Cox</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Δ</mi>\u0000 <mo>;</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>${rm Cox}^{(k)}(X,Delta;x)$</annotation>\u0000 </semantics></math> of a klt singularity stabilizes for <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> large enough. The second result is a boundedness one, we prove that for an <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional klt singularity <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Δ</mi>\u0000 <mo>;</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,Delta;x)$</annotation>\u0000 </semantics></math>, the iteration of Cox rings stabilizes for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>⩾</mo>\u0000 <mi>c</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$kgeqslant c(n)$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 ","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139655253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The second variation of the Hodge norm and higher Prym representations
霍奇规范的第二种变化和更高的普赖姆表征
IF 1.1
2区 数学
Vladimir Marković, Ognjen Tošić
{"title":"The second variation of the Hodge norm and higher Prym representations","authors":"Vladimir Marković, Ognjen Tošić","doi":"10.1112/topo.12322","DOIUrl":"https://doi.org/10.1112/topo.12322","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>Σ</mi>\u0000 <mi>h</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$chi in H^1(Sigma _h,mathbb {Q})$</annotation>\u0000 </semantics></math> denote a rational cohomology class, and let <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>H</mo>\u0000 <mi>χ</mi>\u0000 </msub>\u0000 <annotation>$operatorname{H}_chi$</annotation>\u0000 </semantics></math> denote its Hodge norm. We recover the result that <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>H</mo>\u0000 <mi>χ</mi>\u0000 </msub>\u0000 <annotation>$operatorname{H}_chi$</annotation>\u0000 </semantics></math> is a plurisubharmonic function on the Teichmüller space <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mi>h</mi>\u0000 </msub>\u0000 <annotation>${mathcal {T}}_h$</annotation>\u0000 </semantics></math>, and characterize complex directions along which the complex Hessian of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>H</mo>\u0000 <mi>χ</mi>\u0000 </msub>\u0000 <annotation>$operatorname{H}_chi$</annotation>\u0000 </semantics></math> vanishes. Moreover, we find examples of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>Σ</mi>\u0000 <mi>h</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$chi in H^1(Sigma _{h},mathbb {Q})$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>H</mo>\u0000 <mi>χ</mi>\u0000 </msub>\u0000 <annotation>$operatorname{H}_chi$</annotation>\u0000 </semantics></math> is not strictly plurisubharmonic. As part of this construction, we find an unbranched covering <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>π</mi>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>Σ</mi","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139655308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost strict domination and anti-de Sitter 3-manifolds
几乎严格的支配与反德西特3-漫游
IF 1.1
2区 数学
Nathaniel Sagman
{"title":"Almost strict domination and anti-de Sitter 3-manifolds","authors":"Nathaniel Sagman","doi":"10.1112/topo.12323","DOIUrl":"https://doi.org/10.1112/topo.12323","url":null,"abstract":"<p>We define a condition called almost strict domination for pairs of representations <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>→</mo>\u0000 <mi>PSL</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$rho _1:pi _1(S_{g,n})rightarrow textrm {PSL}(2,mathbb {R})$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>→</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation>$rho _2:pi _1(S_{g,n})rightarrow G$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is the isometry group of a Hadamard manifold, and prove that it holds if and only if one can find a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(rho _1,rho _2)$</annotation>\u0000 </semantics></math>-equivariant spacelike maximal surface in a certain pseudo-Riemannian manifold, unique up to fixing some parameters. The proof amounts to setting up and solving an interesting variati","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139655309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic theories of power operations
幂运算的代数理论
IF 1.1
2区 数学
William Balderrama
{"title":"Algebraic theories of power operations","authors":"William Balderrama","doi":"10.1112/topo.12318","DOIUrl":"https://doi.org/10.1112/topo.12318","url":null,"abstract":"<p>We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$mathbb {E}_infty$</annotation>\u0000 </semantics></math> ring spectra. In particular, we consider Quillen cohomology in the context of algebras over algebraic theories, plethories, and Koszul resolutions for algebras over additive theories. By combining this general algebra with obstruction-theoretic machinery, we obtain tools for computing with <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$mathbb {E}_infty$</annotation>\u0000 </semantics></math> algebras over <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_p$</annotation>\u0000 </semantics></math> and over Lubin–Tate spectra. As an application, we demonstrate the existence of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$mathbb {E}_infty$</annotation>\u0000 </semantics></math> periodic complex orientations at heights <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>⩽</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$hleqslant 2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 4","pages":"1543-1640"},"PeriodicalIF":1.1,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12318","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138485142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Trace embeddings from zero surgery homeomorphisms
从零手术同胚跟踪嵌入
IF 1.1
2区 数学
Kai Nakamura
{"title":"Trace embeddings from zero surgery homeomorphisms","authors":"Kai Nakamura","doi":"10.1112/topo.12319","DOIUrl":"https://doi.org/10.1112/topo.12319","url":null,"abstract":"<p>Manolescu and Piccirillo (2023) recently initiated a program to construct an exotic <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$S^4$</annotation>\u0000 </semantics></math> or <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>#</mo>\u0000 <mi>n</mi>\u0000 <msup>\u0000 <mi>CP</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$# n mathbb {CP}^2$</annotation>\u0000 </semantics></math> by using zero surgery homeomorphisms and Rasmussen's <math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-invariant. They find five knots that if any were slice, one could construct an exotic <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$S^4$</annotation>\u0000 </semantics></math> and disprove the Smooth 4-dimensional Poincaré conjecture. We rule out this exciting possibility and show that these knots are not slice. To do this, we use a zero surgery homeomorphism to relate slice properties of two knots <i>stably</i> after a connected sum with some 4-manifold. Furthermore, we show that our techniques will extend to the entire infinite family of zero surgery homeomorphisms constructed by Manolescu and Piccirillo. However, our methods do not completely rule out the possibility of constructing an exotic <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$S^4$</annotation>\u0000 </semantics></math> or <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>#</mo>\u0000 <mi>n</mi>\u0000 <msup>\u0000 <mi>CP</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$# n mathbb {CP}^2$</annotation>\u0000 </semantics></math> as Manolescu and Piccirillo proposed. We explain the limits of these methods hoping this will inform and invite new attempts to construct an exotic <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$S^4$</annotation>\u0000 </semantics></math> or <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>#</mo>\u0000 <mi>n</mi>\u0000 <msup>\u0000 <mi>CP</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$# n mathbb {CP}^2$</annotation>\u0000 </semantics></math>. We also show that a family of homotopy spheres constructed by Manolescu and Picc","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 4","pages":"1641-1664"},"PeriodicalIF":1.1,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138485143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Asymptotic and Assouad–Nagata dimension of finitely generated groups and their subgroups
有限生成群及其子群的渐近维数和副长维数
IF 1.1
2区 数学
Levi Sledd
{"title":"Asymptotic and Assouad–Nagata dimension of finitely generated groups and their subgroups","authors":"Levi Sledd","doi":"10.1112/topo.12314","DOIUrl":"https://doi.org/10.1112/topo.12314","url":null,"abstract":"<p>We prove that for all <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 <mo>∪</mo>\u0000 <mo>{</mo>\u0000 <mi>∞</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$k,m,n in mathbb {N} cup lbrace infty rbrace$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>⩽</mo>\u0000 <mi>k</mi>\u0000 <mo>⩽</mo>\u0000 <mi>m</mi>\u0000 <mo>⩽</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$4 leqslant k leqslant m leqslant n$</annotation>\u0000 </semantics></math>, there exists a finitely generated group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> with a finitely generated subgroup <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>asdim</mo>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{asdim}(G) = k$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>asdim</mo>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{asdim}_{textnormal {AN}}(G) = m$</annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>asdim</mo>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$operatorname{asdim}_{textnormal {AN}}(H)=n$</annotation>\u0000 </semantics></math>. This simultaneously answers two open questions in asymptotic dimension theory.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 4","pages":"1509-1542"},"PeriodicalIF":1.1,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138480904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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