Journal of Topology最新文献

{"title":"Cubulating surface-by-free groups","authors":"Mahan Mj","doi":"10.1112/topo.70011","DOIUrl":"https://doi.org/10.1112/topo.70011","url":null,"abstract":"<p>Let\u0000\u0000 </p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861375","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}

{"title":"Nonabelian basechange theorems and étale homotopy theory","authors":"Peter J. Haine,&nbsp;Tim Holzschuh,&nbsp;Sebastian Wolf","doi":"10.1112/topo.70009","DOIUrl":"https://doi.org/10.1112/topo.70009","url":null,"abstract":"<p>This paper has two main goals. First, we prove nonabelian refinements of basechange theorems in étale cohomology (i.e., prove analogues of the classical statements for sheaves of <i>spaces</i>). Second, we apply these theorems to prove a number of results about the étale homotopy type. Specifically, we prove nonabelian refinements of the smooth basechange theorem, Huber–Gabber affine analogue of the proper basechange theorem, and Fujiwara–Gabber rigidity theorem. Our methods also recover Chough's nonabelian refinement of the proper basechange theorem. Transporting an argument of Bhatt–Mathew to the nonabelian setting, we apply nonabelian proper basechange to show that the profinite étale homotopy type satisfies arc-descent. Using nonabelian smooth and proper basechange and descent, we give rather soft proofs of a number of Künneth formulas for the étale homotopy type.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762241","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}

{"title":"Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology","authors":"Irving Dai,&nbsp;Matthew Hedden,&nbsp;Abhishek Mallick,&nbsp;Matthew Stoffregen","doi":"10.1112/topo.70008","DOIUrl":"https://doi.org/10.1112/topo.70008","url":null,"abstract":"<p>We show that a large class of satellite operators are rank-expanding; that is, they map some rank-one subgroup of the concordance group onto an infinite linearly independent set. Our work constitutes the first systematic study of this property in the literature and partially affirms a conjecture of the second author and Pinzón-Caicedo. More generally, we establish a Floer-theoretic condition for a family of companion knots to have infinite-rank image under satellites from this class. The methods we use are amenable to patterns that act trivially in topological concordance and are capable of handling a surprisingly wide variety of companions. For instance, we give an infinite linearly independent family of Whitehead doubles whose companion knots all have negative <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-invariant. Our results also recover and extend several theorems in this area established using instanton Floer homology.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737409","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}

{"title":"Chow–Witt rings and topology of flag varieties","authors":"Thomas Hudson,&nbsp;Ákos K. Matszangosz,&nbsp;Matthias Wendt","doi":"10.1112/topo.70004","DOIUrl":"https://doi.org/10.1112/topo.70004","url":null,"abstract":"<p>The paper computes the Witt-sheaf cohomology rings of partial flag varieties in type A in terms of the Pontryagin classes of the subquotient bundles. The proof is based on a Leray–Hirsch-type theorem for Witt-sheaf cohomology for the maximal rank cases, and a detailed study of cohomology ring presentations and annihilators of characteristic classes for the general case. The computations have consequences for the topology of real flag manifolds: we show that all torsion in the integral cohomology is 2-torsion, which was not known in full generality previously. This allows for example to compute the Poincaré polynomials of complete flag varieties for cohomology with twisted integer coefficients. The computations also allow to describe the Chow–Witt rings of flag varieties, and we sketch an enumerative application to counting flags satisfying multiple incidence conditions to given hypersurfaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665813","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}

{"title":"Recalibrating \u0000 \u0000 R\u0000 $mathbb {R}$\u0000 -order trees and \u0000 \u0000 \u0000 \u0000 Homeo\u0000 +\u0000 \u0000 \u0000 (\u0000 \u0000 S\u0000 1\u0000 \u0000 )\u0000 \u0000 \u0000 $mbox{Homeo}_+(S^1)$\u0000 -representations of link groups","authors":"Steven Boyer,&nbsp;Cameron McA. Gordon,&nbsp;Ying Hu","doi":"10.1112/topo.70005","DOIUrl":"https://doi.org/10.1112/topo.70005","url":null,"abstract":"<p>In this paper, we study the left-orderability of 3-manifold groups using an enhancement, called recalibration, of Calegari and Dunfield's ‘flipping’ construction, used for modifying <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mtext>Homeo</mtext>\u0000 <mo>+</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$text{Homeo}_+(S^1)$</annotation>\u0000 </semantics></math>-representations of the fundamental groups of closed 3-manifolds. The added flexibility accorded by recalibration allows us to produce <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mtext>Homeo</mtext>\u0000 <mo>+</mo>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$text{Homeo}_+(S^1)$</annotation>\u0000 </semantics></math>-representations of hyperbolic link exteriors so that a chosen element in the peripheral subgroup is sent to any given rational rotation. We apply these representations to show that the branched covers of families of links associated to epimorphisms of the link group onto a finite cyclic group are left-orderable. This applies, for instance, to fibred hyperbolic strongly quasi-positive links. Our result on the orderability of branched covers implies that the degeneracy locus of any pseudo-Anosov flow on an alternating knot complement must be meridional, which generalises the known result that the fractional Dehn twist coefficient of any hyperbolic fibred alternating knot is zero. Applications of these representations to order detection of slopes are also discussed in the paper.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664955","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}

{"title":"Equivariant algebraic concordance of strongly invertible knots","authors":"Alessio Di Prisa","doi":"10.1112/topo.70006","DOIUrl":"https://doi.org/10.1112/topo.70006","url":null,"abstract":"<p>By considering a particular type of invariant Seifert surfaces we define a homomorphism <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> from the (topological) equivariant concordance group of directed strongly invertible knots <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>C</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <annotation>$widetilde{mathcal {C}}$</annotation>\u0000 </semantics></math> to a new equivariant algebraic concordance group <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mover>\u0000 <mi>G</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mi>Z</mi>\u0000 </msup>\u0000 <annotation>$widetilde{mathcal {G}}^mathbb {Z}$</annotation>\u0000 </semantics></math>. We prove that <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> lifts both Miller and Powell's equivariant algebraic concordance homomorphism (<i>J. Lond. Math. Soc</i>. (2023), no. 107, 2025-2053) and Alfieri and Boyle's equivariant signature (<i>Michigan Math. J. 1</i> (2023), no. 1, 1–17). Moreover, we provide a partial result on the isomorphism type of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mover>\u0000 <mi>G</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mi>Z</mi>\u0000 </msup>\u0000 <annotation>$widetilde{mathcal {G}}^mathbb {Z}$</annotation>\u0000 </semantics></math> and obtain a new obstruction to equivariant sliceness, which can be viewed as an equivariant Fox–Milnor condition. We define new equivariant signatures and using these we obtain novel lower bounds on the equivariant slice genus. Finally, we show that <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> can obstruct equivariant sliceness for knots with Alexander polynomial one.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664938","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}

{"title":"Metrics of positive Ricci curvature on simply-connected manifolds of dimension \u0000 \u0000 \u0000 6\u0000 k\u0000 \u0000 $6k$","authors":"Philipp Reiser","doi":"10.1112/topo.70007","DOIUrl":"https://doi.org/10.1112/topo.70007","url":null,"abstract":"<p>A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply-connected 6-manifold admits a Riemannian metric of positive scalar curvature. For metrics of positive Ricci curvature, it is widely open whether a similar result holds; there are no obstructions known for those manifolds to admit a metric of positive Ricci curvature, while the number of examples known is limited. In this article, we introduce a new description of certain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$6k$</annotation>\u0000 </semantics></math>-dimensional manifolds via labeled bipartite graphs and use an earlier result of the author to construct metrics of positive Ricci curvature on these manifolds. In this way, we obtain many new examples, both spin and nonspin, of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$6k$</annotation>\u0000 </semantics></math>-dimensional manifolds with a metric of positive Ricci curvature.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664918","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}

{"title":"On the equivalence of Lurie's \u0000 \u0000 ∞\u0000 $infty$\u0000 -operads and dendroidal \u0000 \u0000 ∞\u0000 $infty$\u0000 -operads","authors":"Vladimir Hinich,&nbsp;Ieke Moerdijk","doi":"10.1112/topo.70003","DOIUrl":"https://doi.org/10.1112/topo.70003","url":null,"abstract":"<p>In this paper, we prove the equivalence of two symmetric monoidal <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-categories of <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-operads, the one defined in Lurie [Higher algebra, available at the author's homepage, http://math.ias.edu/~lurie/, September 2017 version] and the one based on dendroidal spaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565475","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}

{"title":"Geometry of symplectic flux and Lagrangian torus fibrations","authors":"Egor Shelukhin,&nbsp;Dmitry Tonkonog,&nbsp;Renato Vianna","doi":"10.1112/topo.70002","DOIUrl":"https://doi.org/10.1112/topo.70002","url":null,"abstract":"<p>Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the invariant is its concavity over isotopies with linear flux. We derive constraints on flux, Weinstein neighbourhood embeddings and holomorphic disk potentials for Gelfand–Cetlin fibres of Fano varieties in terms of their polytopes. We also describe the space of fibres of almost toric fibrations on the complex projective plane up to Hamiltonian isotopy, and provide other applications.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142524906","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}

{"title":"The Lubin–Tate theory of configuration spaces: I","authors":"D. Lukas B. Brantner,&nbsp;Jeremy Hahn,&nbsp;Ben Knudsen","doi":"10.1112/topo.70000","DOIUrl":"https://doi.org/10.1112/topo.70000","url":null,"abstract":"<p>We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math>-theory, of unordered configuration spaces and identify its <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>${mathrm{E}^2}$</annotation>\u0000 </semantics></math>-page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math>-theory of the weight <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> summands of iterated loop spaces of spheres (parameterizing the weight <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> operations on <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathbb {E}_n$</annotation>\u0000 </semantics></math>-algebras), as well as the <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math>-theory of the configuration spaces of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> points on a punctured surface. We read off the corresponding Morava <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory groups, which appear in a conjecture by Ravenel. Finally, we compute the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_p$</annotation>\u0000 </semantics></math>-homology of the space of unordered configurations of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> particles on a punctured surface.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142524659","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}