发布求助
文献互助 智能选刊 最新文献

Algebraic and Geometric Topology最新文献

筛选
英文 中文
Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion 通过Fox演算和Reidemeister扭转Kuperberg不变量
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-10-25 DOI: 10.2140/agt.2022.22.2419
Daniel López Neumann
{"title":"Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion","authors":"Daniel López Neumann","doi":"10.2140/agt.2022.22.2419","DOIUrl":"https://doi.org/10.2140/agt.2022.22.2419","url":null,"abstract":"We study Kuperberg invariants for sutured manifolds in the case of a semidirect product of an involutory Hopf superalgebra $H$ with its automorphism group $text{Aut}(H)$. These are topological invariants of balanced sutured 3-manifolds endowed with an homomorphism of the fundamental group into $text{Aut}(H)$ and possibly with a $text{Spin}^c$ structure and an homology orientation. We show that these invariants are computed via a form of Fox calculus and that, if $H$ is $mathbb{N}$-graded, they can be extended in a canonical way to polynomial invariants. When $H$ is an exterior algebra, we show that this invariant specializes to a refinement of the twisted relative Reidemeister torsion of sutured 3-manifolds. We also give an explanation of our Fox calculus formulas in terms of a particular Hopf group-algebra.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83190117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Cohomology of Sheaves 捆的上同调
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-02-01 DOI: 10.1142/9789811245039_0013
J. Warner
{"title":"Cohomology of Sheaves","authors":"J. Warner","doi":"10.1142/9789811245039_0013","DOIUrl":"https://doi.org/10.1142/9789811245039_0013","url":null,"abstract":"Let A be an abelian category. Definition 1.1. A complex in A, A•, is a collection of objects A, i ∈ Z and boundary morphisms d : A → A such that d ◦ d = 0 for all i ∈ Z. If A• and B• are complexes, a map f : A• → B• is a collection morphisms f i : A → B commuting with the boundary morphisms. Two maps f, g : A• → B• are said to be homotopic if there are morphisms k : A → Bi−1 such that f i − g = di−1 B ◦ k + kdA. Two complexes are homotopy equivalent if there exist maps f : A• → B• and g : B• → A• such that the compositions are homotopic to the appropriate identity map.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75914883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Homology and Cohomology of CW Complexes CW配合物的同源性和上同源性
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-02-01 DOI: 10.1142/9789811245039_0006
{"title":"Homology and Cohomology of CW Complexes","authors":"","doi":"10.1142/9789811245039_0006","DOIUrl":"https://doi.org/10.1142/9789811245039_0006","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88930841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Čech Cohomology with Values in a Presheaf Čech与预表中值的上同调
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-02-01 DOI: 10.1142/9789811245039_0009
{"title":"Čech Cohomology with Values in a Presheaf","authors":"","doi":"10.1142/9789811245039_0009","DOIUrl":"https://doi.org/10.1142/9789811245039_0009","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"60 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84870744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Presheaves and Sheaves; Basics 预压轴和预压轴;基础知识
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-02-01 DOI: 10.1142/9789811245039_0008
{"title":"Presheaves and Sheaves; Basics","authors":"","doi":"10.1142/9789811245039_0008","DOIUrl":"https://doi.org/10.1142/9789811245039_0008","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82318633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Universal Coefficient Theorems 泛系数定理
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2022-02-01 DOI: 10.1007/978-3-319-46143-4_7
Andrei T. Patrascu
{"title":"Universal Coefficient Theorems","authors":"Andrei T. Patrascu","doi":"10.1007/978-3-319-46143-4_7","DOIUrl":"https://doi.org/10.1007/978-3-319-46143-4_7","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"156 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/978-3-319-46143-4_7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72416729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Infinite families of higher torsion in the homotopy groups of Moore spaces 摩尔空间同伦群中的无限高扭转族
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-11-06 DOI: 10.2140/agt.2023.23.2389
Steven Amelotte, F. Cohen, Y. Luo
{"title":"Infinite families of higher torsion in the homotopy groups of Moore spaces","authors":"Steven Amelotte, F. Cohen, Y. Luo","doi":"10.2140/agt.2023.23.2389","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2389","url":null,"abstract":"We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite $v_1$-periodic families of elements of order $p^{r+1}$ in the homotopy groups of mod $p^r$ Moore spaces. For odd primes $p$, our splitting implies that the homotopy groups of the mod $p^{r+1}$ Moore spectrum are summands of the unstable homotopy groups of each mod $p^r$ Moore space.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"87 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72970310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Projection complexes and quasimedian maps 投影复合体和准中间地图
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-08-30 DOI: 10.2140/agt.2022.22.3277
M. Hagen, H. Petyt
{"title":"Projection complexes and quasimedian maps","authors":"M. Hagen, H. Petyt","doi":"10.2140/agt.2022.22.3277","DOIUrl":"https://doi.org/10.2140/agt.2022.22.3277","url":null,"abstract":"We use the projection complex machinery of Bestvina--Bromberg--Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and its associated hyperbolic spaces are quasiisometric to trees, then the group is quasiisometric to a finite-dimensional CAT(0) cube complex. We deduce various properties, including the Helly property for hierarchically quasiconvex subsets.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87098624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Homotopy types of gauge groups over Riemann surfaces 黎曼曲面上规范群的同伦类型
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-07-31 DOI: 10.2140/agt.2023.23.2309
Masaki Kameko, D. Kishimoto, Masahiro Takeda
{"title":"Homotopy types of gauge groups over Riemann surfaces","authors":"Masaki Kameko, D. Kishimoto, Masahiro Takeda","doi":"10.2140/agt.2023.23.2309","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2309","url":null,"abstract":"Let $G$ be a compact connected Lie group with $pi_1(G)congmathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of the moduli spaces of stable vector bundles over Riemann surfaces.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"249 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77624239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Diffeomorphisms of odd-dimensional discs, glued into a manifold 粘在歧管中的奇维圆盘的微分同态
IF 0.7 3区 数学
Algebraic and Geometric Topology Pub Date : 2021-07-02 DOI: 10.2140/agt.2023.23.2329
Johannes Ebert
{"title":"Diffeomorphisms of odd-dimensional discs, glued into a manifold","authors":"Johannes Ebert","doi":"10.2140/agt.2023.23.2329","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2329","url":null,"abstract":"For a compact $(2n+1)$-dimensional smooth manifold, let $mu_M : B Diff_partial (D^{2n+1}) to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and Hsiang, the rational homotopy groups and the rational homology of $ B Diff_partial (D^{2n+1})$ are known in the concordance stable range. We prove two results on the behaviour of the map $mu_M$ in the concordance stable range. Firstly, it is emph{injective} on rational homotopy groups, and secondly, it is emph{trivial} on rational homology, if $M$ contains sufficiently many embedded copies of $S^ntimes S^{n+1} setminus int(D^{2n+1})$. The homotopical statement is probably not new and follows from the theory of smooth torsion invariants. The homological statement relies on work by Botvinnik and Perlmutter on diffeomorphism of odd-dimensional manifolds.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73344606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信