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Global rigidity of some abelian-by-cyclic groupactions on 𝕋2 𝕋2上一些阿贝尔环群的整体刚性
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-09-23 DOI: 10.2140/gt.2021.25.3133
Sebastián Hurtado, Jinxin Xue
{"title":"Global rigidity of some abelian-by-cyclic group\u0000actions on 𝕋2","authors":"Sebastián Hurtado, Jinxin Xue","doi":"10.2140/gt.2021.25.3133","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3133","url":null,"abstract":"For groups of diffeomorphisms of $T^2$ containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on $T^2$ up to both topological conjugacy and smooth conjugacy under mild assumptions. Along the way, we also prove a Tits alternative type theorem for some groups of diffeomorphisms of $T^2$.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"17 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90753929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 2
Betti realization of varieties defined by formal Laurent series 由正式洛朗级数定义的变种的贝蒂实现
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-09-06 DOI: 10.2140/gt.2021.25.1919
Piotr Achinger, Mattia Talpo
{"title":"Betti realization of varieties defined by formal Laurent series","authors":"Piotr Achinger, Mattia Talpo","doi":"10.2140/gt.2021.25.1919","DOIUrl":"https://doi.org/10.2140/gt.2021.25.1919","url":null,"abstract":"We give two constructions of functorial topological realizations for schemes of finite type over the field $mathbb{C}(!(t)!)$ of formal Laurent series with complex coefficients, with values in the homotopy category of spaces over the circle. The problem of constructing such a realization was stated by D. Treumann, motivated by certain questions in mirror symmetry. The first construction uses spreading out and the usual Betti realization over $mathbb{C}$. The second uses generalized semistable models and log Betti realization defined by Kato and Nakayama, and applies to smooth rigid analytic spaces as well. We provide comparison theorems between the two constructions and relate them to the etale homotopy type and de Rham cohomology. As an illustration of the second construction, we treat two examples, the Tate curve and the non-archimedean Hopf surface.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"451 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86860616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
On the top-dimensional cohomology groups ofcongruence subgroups of SL(n, ℤ) 关于SL(n, n)的同余子群的顶维上同调群
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-09-05 DOI: 10.2140/GT.2021.25.999
Jeremy Miller, Peter Patzt, Andrew Putman
{"title":"On the top-dimensional cohomology groups of\u0000congruence subgroups of SL(n, ℤ)","authors":"Jeremy Miller, Peter Patzt, Andrew Putman","doi":"10.2140/GT.2021.25.999","DOIUrl":"https://doi.org/10.2140/GT.2021.25.999","url":null,"abstract":"Let $Gamma_n(p)$ be the level-$p$ principal congruence subgroup of $text{SL}_n(mathbb{Z})$. Borel-Serre proved that the cohomology of $Gamma_n(p)$ vanishes above degree $binom{n}{2}$. We study the cohomology in this top degree $binom{n}{2}$. Let $mathcal{T}_n(mathbb{Q})$ denote the Tits building of $text{SL}_n(mathbb{Q})$. Lee-Szczarba conjectured that $H^{binom{n}{2}}(Gamma_n(p))$ is isomorphic to $widetilde{H}_{n-2}(mathcal{T}_n(mathbb{Q})/Gamma_n(p))$ and proved that this holds for $p=3$. We partially prove and partially disprove this conjecture by showing that a natural map $H^{binom{n}{2}}(Gamma_n(p)) rightarrow widetilde{H}_{n-2}(mathcal{T}_n(mathbb{Q})/Gamma_n(p))$ is always surjective, but is only injective for $p leq 5$. In particular, we completely calculate $H^{binom{n}{2}}(Gamma_n(5))$ and improve known lower bounds for the ranks of $H^{binom{n}{2}}(Gamma_n(p))$ for $p geq 5$.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"41 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80735727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 8
On the geometry of asymptotically flat manifolds 渐近平面流形的几何性质
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-08-20 DOI: 10.2140/gt.2021.25.2469
Xiuxiong Chen, Yu Li
{"title":"On the geometry of asymptotically flat manifolds","authors":"Xiuxiong Chen, Yu Li","doi":"10.2140/gt.2021.25.2469","DOIUrl":"https://doi.org/10.2140/gt.2021.25.2469","url":null,"abstract":"In this paper, we investigate the geometry of asymptotically flat manifolds with controlled holonomy. We show that any end of such manifold admits a refined torus fibration over an ALE manifold. In addition, we prove a Hitchin-Thorpe inequality for oriented Ricci-flat $4$-manifolds with curvature decay and controlled holonomy. As an application, we show that any complete asymptotically flat Ricci-flat metric on a $4$-manifold which is homeomorphic to $mathbb R^4$ must be isometric to the Euclidean or the Taub-NUT metric, provided that the tangent cone at infinity is not $mathbb R times mathbb R_+$.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"27 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89905089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The Legendrian Whitney trick 传说中的惠特尼把戏
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-08-13 DOI: 10.2140/gt.2021.25.3229
Roger Casals, Dishant M. Pancholi, F. Presas
{"title":"The Legendrian Whitney trick","authors":"Roger Casals, Dishant M. Pancholi, F. Presas","doi":"10.2140/gt.2021.25.3229","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3229","url":null,"abstract":"In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"29 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86245741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 11
Positive scalar curvature on manifolds with odd order abelian fundamental groups 奇阶阿贝尔基本群流形上的正标量曲率
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-08-02 DOI: 10.2140/GT.2021.25.497
B. Hanke
{"title":"Positive scalar curvature on manifolds with odd order abelian fundamental groups","authors":"B. Hanke","doi":"10.2140/GT.2021.25.497","DOIUrl":"https://doi.org/10.2140/GT.2021.25.497","url":null,"abstract":"We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which have odd order abelian fundamental groups, are non-spin and atoral. This solves the Gromov-Lawson-Rosenberg conjecture for a new class of manifolds with finite fundamental groups.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"116 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78284378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5
A refinement of Khovanov homology Khovanov同调的一个改进
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-07-31 DOI: 10.2140/gt.2021.25.1861
A. Lobb, Liam Watson
{"title":"A refinement of Khovanov homology","authors":"A. Lobb, Liam Watson","doi":"10.2140/gt.2021.25.1861","DOIUrl":"https://doi.org/10.2140/gt.2021.25.1861","url":null,"abstract":"We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"181 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80271408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 11
The cohomology rings of smooth toric varieties and quotients of moment-angle complexes 光滑环型的上同环和矩角配合物的商
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-07-10 DOI: 10.2140/gt.2021.25.2109
M. Franz
{"title":"The cohomology rings of smooth toric varieties and quotients of moment-angle complexes","authors":"M. Franz","doi":"10.2140/gt.2021.25.2109","DOIUrl":"https://doi.org/10.2140/gt.2021.25.2109","url":null,"abstract":"Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a torsion product involving the corresponding Stanley-Reisner ring. We show that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. We rectify this by defining an explicit deformation of the canonical multiplication on the torsion product.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"43 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81528946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 17
Commensurating HNN extensions: nonpositive curvature and biautomaticity 通约HNN扩展:非正曲率和双自动性
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-07-08 DOI: 10.2140/gt.2021.25.1819
I. Leary, A. Minasyan
{"title":"Commensurating HNN extensions: nonpositive curvature and biautomaticity","authors":"I. Leary, A. Minasyan","doi":"10.2140/gt.2021.25.1819","DOIUrl":"https://doi.org/10.2140/gt.2021.25.1819","url":null,"abstract":"We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"235 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76627252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 27
On the topology and the boundary ofN–dimensional RCD(K,N) spaces 关于N维RCD(K,N)空间的拓扑和边界
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-07-04 DOI: 10.2140/GT.2021.25.445
V. Kapovitch, A. Mondino
{"title":"On the topology and the boundary of\u0000N–dimensional RCD(K,N) spaces","authors":"V. Kapovitch, A. Mondino","doi":"10.2140/GT.2021.25.445","DOIUrl":"https://doi.org/10.2140/GT.2021.25.445","url":null,"abstract":"We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"20 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78655833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 41
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