arXiv: Algebraic Topology最新文献_第5页

How many simplices are needed to triangulate a Grassmannian? 三角测量格拉斯曼人需要多少个简单函数?

arXiv: Algebraic Topology Pub Date : 2020-01-22 DOI: 10.12775/tmna.2020.027

Dejan Govc, W. Marzantowicz, Petar Pavešić

引用次数: 11

Flatness and Shipley’s algebraicization theorem 平面性和希普利代数定理

arXiv: Algebraic Topology Pub Date : 2020-01-18 DOI: 10.4310/hha.2021.v23.n1.a11

J. Williamson

引用次数: 4

Computation of Nielsen and Reidemeister coincidence numbers for multiple maps 多个地图的Nielsen和Reidemeister符合数的计算

arXiv: Algebraic Topology Pub Date : 2020-01-18 DOI: 10.12775/tmna.2020.002

Tha'is F. M. Monis, P. Wong

引用次数: 0

The bivariant parasimplicial $mathsf{S}_{bullet}$-construction 二元拟隐$mathsf{S}_{bullet}$-构造

arXiv: Algebraic Topology Pub Date : 2020-01-11 DOI: 10.25926/kj82-kr40

F. Beckert

{"title":"The bivariant parasimplicial $mathsf{S}_{bullet}$-construction","authors":"F. Beckert","doi":"10.25926/kj82-kr40","DOIUrl":"https://doi.org/10.25926/kj82-kr40","url":null,"abstract":"Coherent strings of composable morphisms play an important role in various important constructions in abstract stable homotopy theory (for example algebraic K-theory or higher Toda brackets) and in the representation theory of finite dimensional algebras (as representations of Dynkin quivers of type A). In a first step we will prove a strong comparison result relating composable strings of morphisms and coherent diagrams on cubes with support on a path from the initial to the final object. \u0000We observe that both structures are equivalent (by passing to higher analogues of mesh categories) to distinguished coherent diagrams on special classes of morphism objects in the 2-category of parasimplices. Furthermore, we show that the notion of distinguished coherent diagrams generalizes well to arbitrary morphism objects in this 2-category. The resulting categories of coherent diagrams lead to higher versions of the $mathsf{S}_{bullet}$-construction and are closely related to representations of higher Auslander algebras of Dynkin quivers of type A. \u0000Understanding these categories and the functors relating them in general will require a detailed analysis of the 2-category of parasimplices as well as basic results from abstract cubical homotopy theory (since subcubes of distinguished diagrams very often turn out to be bicartesian). Finally, we show that the previous comparison result extends to a duality theorem on general categories of distinguished coherent diagrams, as a special case leading to some new derived equivalences between higher Auslander algebras.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75319230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Decomposition of Twisted Equivariant K-Theory 扭曲等变k理论的一个分解

arXiv: Algebraic Topology Pub Date : 2020-01-07 DOI: 10.3842/SIGMA.2021.041

J. M. G'omez, J. Ram'irez

引用次数: 1

A guide to tensor-triangular classification 张量-三角形分类指南

arXiv: Algebraic Topology Pub Date : 2019-12-19 DOI: 10.1201/9781351251624-4

Paul Balmer

引用次数: 14

On the James and Hilton-Milnor Splittings, & the metastable EHP sequence. 论詹姆斯分裂和希尔顿-米尔诺分裂，以及亚稳态EHP序列。

arXiv: Algebraic Topology Pub Date : 2019-12-09 DOI: 10.25537/dm.2021v26.1423-1464

Sanath K. Devalapurkar, Peter J. Haine

{"title":"On the James and Hilton-Milnor Splittings, & the metastable EHP sequence.","authors":"Sanath K. Devalapurkar, Peter J. Haine","doi":"10.25537/dm.2021v26.1423-1464","DOIUrl":"https://doi.org/10.25537/dm.2021v26.1423-1464","url":null,"abstract":"This note provides modern proofs of some classical results in algebraic topology, such as the James Splitting, the Hilton-Milnor Splitting, and the metastable EHP sequence. We prove fundamental splitting results begin{equation*} Sigma Omega Sigma X simeq Sigma X vee (Xwedge SigmaOmega Sigma X) quad text{and} quad Omega(X vee Y) simeq Omega Xtimes Omega Ytimes Omega Sigma(Omega X wedge Omega Y) end{equation*} in the maximal generality of an $infty$-category with finite limits and pushouts in which pushouts squares remain pushouts after basechange along an arbitrary morphism (i.e., Mather's Second Cube Lemma holds). For connected objects, these imply the classical James and Hilton-Milnor Splittings. Moreover, working in this generality shows that the James and Hilton-Milnor splittings hold in many new contexts, for example in: elementary $infty$-topoi, profinite spaces, and motivic spaces over arbitrary base schemes. The splitting result in this last context extend Wickelgren and Williams' splitting result for motivic spaces over a perfect field. We also give two proofs of the metastable EHP sequence in the setting of $infty$-topoi: the first is a new, non-computational proof that only utilizes basic connectedness estimates involving the James filtration and the Blakers-Massey Theorem, while the second reduces to the classical computational proof.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75886126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

SEQUENTIAL COLLISION-FREE OPTIMAL MOTION PLANNING ALGORITHMS IN PUNCTURED EUCLIDEAN SPACES 穿孔欧几里得空间中顺序无碰撞最优运动规划算法

arXiv: Algebraic Topology Pub Date : 2019-12-09 DOI: 10.1017/s0004972720000167

Cesar A. IPANAQUE ZAPATA, Jes'us Gonz'alez

引用次数: 1

Sectional category and the fixed point property 分段范畴与不动点性质

arXiv: Algebraic Topology Pub Date : 2019-12-07 DOI: 10.12775/tmna.2020.033

C. A. I. Zapata, Jes'us Gonz'alez

引用次数: 3

Decomposition spaces and poset-stratified spaces 分解空间和后分层空间

arXiv: Algebraic Topology Pub Date : 2019-12-01 DOI: 10.32513/tbilisi/1593223222

Shoji Yokura

{"title":"Decomposition spaces and poset-stratified spaces","authors":"Shoji Yokura","doi":"10.32513/tbilisi/1593223222","DOIUrl":"https://doi.org/10.32513/tbilisi/1593223222","url":null,"abstract":"In 1920s R. L. Moore introduced emph{upper semicontinuous} and emph{lower semicontinuous} decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in 1950s. In this paper we consider lower semicontinuous decompositions $mathcal D$ of a topological space $X$ such that the decomposition spaces $X/mathcal D$ are Alexandroff spaces. If the associated proset (preordered set) of the decomposition space $X/mathcal D$ is a poset, then the decomposition map $pi:X to X/mathcal D$ is emph{a continuous map from the topological space $X$ to the poset $X/mathcal D$ with the associated Alexandroff topology}, which is nowadays called emph{a poset-stratified space}. As an application, we capture the face poset of a real hyperplane arrangement $mathcal A$ of $mathbb R^n$ as the associated poset of the decomposition space $mathbb R^n/mathcal D(mathcal A)$ of the decomposition $mathcal D(mathcal A)$ determined by the arrangement $mathcal A$. We also show that for any locally small category $mathcal C$ the set $hom_{mathcal C}(X,Y)$ of morphisms from $X$ to $Y$ can be considered as a poset-stratified space, and that for any objects $S, T$ (where $S$ plays as a source object and $T$ as a target object) there are a covariant functor $frak {st}^S_*: mathcal C to mathcal Strat$ and a contravariant functor $frak {st}^*_T$ $frak {st}^*_T: mathcal C to mathcal Strat$ from $mathcal C$ to the category $mathcal Strat$ of poset-stratified spaces. We also make a remark about Yoneda's Lemmas as to poset-stratified space structures of $hom_{mathcal C}(X,Y)$.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90790172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7