Journal of Topology最新文献_第8页

Semisimple four-dimensional topological field theories cannot detect exotic smooth structure 半简单四维拓扑场论不能检测奇异光滑结构

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-04-11 DOI: 10.1112/topo.12288

David Reutter

{"title":"Semisimple four-dimensional topological field theories cannot detect exotic smooth structure","authors":"David Reutter","doi":"10.1112/topo.12288","DOIUrl":"https://doi.org/10.1112/topo.12288","url":null,"abstract":"We prove that semisimple four-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth four-manifolds and homotopy equivalent simply connected closed oriented smooth four-manifolds. We show that all currently known four-dimensional field theories are semisimple, including unitary field theories, and once-extended field theories which assign algebras or linear categories to 2-manifolds. As an application, we compute the value of a semisimple field theory on a simply connected closed oriented 4-manifold in terms of its Euler characteristic and signature. Moreover, we show that a semisimple four-dimensional field theory is invariant under <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}P^2$</annotation>\u0000 </semantics></math>-stable diffeomorphisms if and only if the Gluck twist acts trivially. This may be interpreted as the absence of fermions amongst the ‘point particles’ of the field theory. Such fermion-free field theories cannot distinguish homotopy equivalent 4-manifolds. Throughout, we illustrate our results with the Crane–Yetter–Kauffman field theory associated to a ribbon fusion category, settling in the negative the question of whether it is sensitive to smooth structure. As a purely algebraic corollary of our results applied to this field theory, we show that a ribbon fusion category contains a fermionic object if and only if its Gauss sums vanish.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 2","pages":"542-566"},"PeriodicalIF":1.1,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12288","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50128639","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

Holonomy of complex projective structures on surfaces with prescribed branch data 具有规定分支数据的曲面上复杂投影结构的完整性

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-03-13 DOI: 10.1112/topo.12287

Thomas Le Fils

引用次数: 0

Augmentations and immersed Lagrangian fillings 增广和浸入式拉格朗日填充

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-02-28 DOI: 10.1112/topo.12280

Yu Pan, Dan Rutherford

{"title":"Augmentations and immersed Lagrangian fillings","authors":"Yu Pan, Dan Rutherford","doi":"10.1112/topo.12280","DOIUrl":"10.1112/topo.12280","url":null,"abstract":"For a Legendrian link <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>J</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$Lambda subset J^1M$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>=</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$M = mathbb {R}$</annotation>\u0000 </semantics></math> or <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$S^1$</annotation>\u0000 </semantics></math>, immersed exact Lagrangian fillings <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>⊂</mo>\u0000 <mtext>Symp</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>J</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>≅</mo>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L subset mbox{Symp}(J^1M) cong T^*(mathbb {R}_{>0} times M)$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mi>Λ</mi>\u0000 <annotation>$Lambda$</annotation>\u0000 </semantics></math> can be lifted to conical Legendrian fillings <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>J</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Sigma subset J^1(mathbb {R}_{>0} times M)$</annotation>\u0000 </semanti","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"368-429"},"PeriodicalIF":1.1,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43551510","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: 7

Toroidal integer homology three-spheres have irreducible S U ( 2 ) $SU(2)$ -representations 环面整数同调三球具有不可约SU(2)$SU(2)$‐表示

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-02-18 DOI: 10.1112/topo.12275

Tye Lidman, Juanita Pinzón-Caicedo, Raphael Zentner

引用次数: 1

Families of diffeomorphisms and concordances detected by trivalent graphs 三价图检测的微分同胚族和调和族

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-02-14 DOI: 10.1112/topo.12283

Boris Botvinnik, Tadayuki Watanabe

{"title":"Families of diffeomorphisms and concordances detected by trivalent graphs","authors":"Boris Botvinnik, Tadayuki Watanabe","doi":"10.1112/topo.12283","DOIUrl":"10.1112/topo.12283","url":null,"abstract":"We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <msub>\u0000 <mi>Diff</mi>\u0000 <mi>∂</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>⊗</mo>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 <annotation>$pi _*(Bmathrm{Diff}_{partial }(D^d))otimes {mathbb {Q}}$</annotation>\u0000 </semantics></math> are lifted to homotopy groups of the moduli space of <math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-cobordisms <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <msub>\u0000 <mi>Diff</mi>\u0000 <mo>⊔</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <mi>I</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>⊗</mo>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 <annotation>$pi _*(Bmathrm{Diff}_{sqcup }(D^dtimes I))otimes {mathbb {Q}}$</annotation>\u0000 </semantics></math>. As a geometrical application, we show that those elements in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <msub>\u0000 <mi>Diff</mi>\u0000 <mi>∂</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 ","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"207-233"},"PeriodicalIF":1.1,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41633462","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: 3

Simplicial volume and essentiality of manifolds fibered over spheres 球体上纤维流形的简单体积和本质

IF 1.1 2区数学

Journal of Topology Pub Date : 2023-02-06 DOI: 10.1112/topo.12286

Thorben Kastenholz, Jens Reinhold

{"title":"Simplicial volume and essentiality of manifolds fibered over spheres","authors":"Thorben Kastenholz, Jens Reinhold","doi":"10.1112/topo.12286","DOIUrl":"10.1112/topo.12286","url":null,"abstract":"We study the question when a manifold that fibers over a sphere can be rationally essential, or have positive simplicial volume. More concretely, we show that mapping tori of manifolds (whose fundamental groups can be quite arbitrary) of dimension <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>⩾</mo>\u0000 <mn>7</mn>\u0000 </mrow>\u0000 <annotation>$2n +1 geqslant 7$</annotation>\u0000 </semantics></math> with non-zero simplicial volume are very common. This contrasts the case of fiber bundles over a sphere of dimension <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 2$</annotation>\u0000 </semantics></math>: we prove that their total spaces are rationally inessential if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 3$</annotation>\u0000 </semantics></math>, and always have simplicial volume 0. Using a result by Dranishnikov, we also deduce a surprising property of macroscopic dimension, and we give two applications to positive scalar curvature and characteristic classes, respectively.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"192-206"},"PeriodicalIF":1.1,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12286","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41675764","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

Heegaard genus and complexity of fibered knots 有纤维结的精梳属和复杂性

IF 1.1 2区数学

Journal of Topology Pub Date : 2022-11-08 DOI: 10.1112/topo.12268

Mustafa Cengiz

{"title":"Heegaard genus and complexity of fibered knots","authors":"Mustafa Cengiz","doi":"10.1112/topo.12268","DOIUrl":"10.1112/topo.12268","url":null,"abstract":"We prove that if a fibered knot <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> with genus greater than 1 in a three-manifold <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> has a sufficiently complicated monodromy, then <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> induces a minimal genus Heegaard splitting <math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math> that is unique up to isotopy, and small genus Heegaard splittings of <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> are stabilizations of <math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math>. We provide a complexity bound in terms of the Heegaard genus of <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2389-2425"},"PeriodicalIF":1.1,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42863430","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

Infinitely many virtual geometric triangulations 无限多个虚拟几何三角形

IF 1.1 2区数学

Journal of Topology Pub Date : 2022-11-01 DOI: 10.1112/topo.12271

David Futer, Emily Hamilton, Neil R. Hoffman

引用次数: 2

Decompositions of the stable module ∞ $infty$ -category 稳定模∞的分解$infty$ -范畴

IF 1.1 2区数学

Journal of Topology Pub Date : 2022-10-29 DOI: 10.1112/topo.12269

Joshua Hunt

{"title":"Decompositions of the stable module \u0000 \u0000 ∞\u0000 $infty$\u0000 -category","authors":"Joshua Hunt","doi":"10.1112/topo.12269","DOIUrl":"10.1112/topo.12269","url":null,"abstract":"We show that the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category of a finite group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> decomposes in three different ways as a limit of the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-categories of certain subgroups of <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category to be defined for any <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-space, then showing that this extension only depends on the <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>-equivariant homotopy type of a <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-space. The methods used are not specific to the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category, so may also be applicable in other settings where an <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category depends functorially on <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2298-2316"},"PeriodicalIF":1.1,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493568","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

Étale cohomology, purity and formality with torsion coefficients Étale上同调，纯度和形式与扭转系数

IF 1.1 2区数学

Journal of Topology Pub Date : 2022-10-27 DOI: 10.1112/topo.12273

Joana Cirici, Geoffroy Horel

引用次数: 11