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On the Whitehead nightmare and some related topics 关于怀特海噩梦和一些相关主题
IF 2.3
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/73
Valentin Poénaru
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引用次数: 0
Rational homotopy via Sullivan models and enriched Lie algebras 通过沙利文模型和丰富的李代数实现理性同调
IF 2.3
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/67
Y. Félix, S. Halperin
{"title":"Rational homotopy via Sullivan models and enriched Lie algebras","authors":"Y. Félix, S. Halperin","doi":"10.4171/emss/67","DOIUrl":"https://doi.org/10.4171/emss/67","url":null,"abstract":"","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"4 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139272299","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
String topology in three flavors 三味弦拓扑
IF 2.3
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/72
Florian Naef, Manuel Rivera, Nathalie Wahl
{"title":"String topology in three flavors","authors":"Florian Naef, Manuel Rivera, Nathalie Wahl","doi":"10.4171/emss/72","DOIUrl":"https://doi.org/10.4171/emss/72","url":null,"abstract":"","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"54 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274963","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
Low-dimensional solenoidal manifolds 低维电磁流形
IF 2.3
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/69
Alberto Verjovsky
{"title":"Low-dimensional solenoidal manifolds","authors":"Alberto Verjovsky","doi":"10.4171/emss/69","DOIUrl":"https://doi.org/10.4171/emss/69","url":null,"abstract":"","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"44 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139275545","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
Singularity formation in the incompressible Euler equation in finite and infinite time 有限时间和无限时间内不可压缩欧拉方程中奇点的形成
IF 2.3
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/66
Theodore D. Drivas, T. Elgindi
{"title":"Singularity formation in the incompressible Euler equation in finite and infinite time","authors":"Theodore D. Drivas, T. Elgindi","doi":"10.4171/emss/66","DOIUrl":"https://doi.org/10.4171/emss/66","url":null,"abstract":"","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"19 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139275110","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
The diagonal of cellular spaces and effective algebro-homotopical constructions 元胞空间的对角线与有效代数同局部结构
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4171/emss/71
Anibal M. Medina-Mardones
{"title":"The diagonal of cellular spaces and effective algebro-homotopical constructions","authors":"Anibal M. Medina-Mardones","doi":"10.4171/emss/71","DOIUrl":"https://doi.org/10.4171/emss/71","url":null,"abstract":"In this survey article we discuss certain homotopy coherent enhancements of the coalgebra structure on cellular chains defined by an approximation to the diagonal. Over the rational numbers, $C_infty$-coalgebra structures control the $mathbb Q$-complete homotopy theory of spaces, and over the integers, $E_infty$-coalgebras provide an appropriate setting to model the full homotopy category. Effective constructions of these structures, the focus of this work, carry geometric and combinatorial information which has found applications in various fields including deformation theory, higher category theory, and condensed matter physics.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"9 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227560","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: 1
On subspace designs 关于子空间设计
EMS Surveys in Mathematical Sciences Pub Date : 2023-11-07 DOI: 10.4171/emss/77
Paolo Santonastaso, Ferdinando Zullo
{"title":"On subspace designs","authors":"Paolo Santonastaso, Ferdinando Zullo","doi":"10.4171/emss/77","DOIUrl":"https://doi.org/10.4171/emss/77","url":null,"abstract":"Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we provide bounds involving the parameters of a subspace design, showing they are tight via explicit constructions. We point out a connection with sum-rank metric codes, dealing with optimal codes and minimal codes with respect to this metric. Applications to two-intersection sets with respect to hyperplanes, two-weight codes, cutting blocking sets and lossless dimension expanders are also provided.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"33 15‐16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432403","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: 4
Chain duality for categories over complexes 复上范畴的链对偶性
EMS Surveys in Mathematical Sciences Pub Date : 2023-10-24 DOI: 10.4171/emss/65
James F. Davis, Carmen Rovi
{"title":"Chain duality for categories over complexes","authors":"James F. Davis, Carmen Rovi","doi":"10.4171/emss/65","DOIUrl":"https://doi.org/10.4171/emss/65","url":null,"abstract":"We show that the additive category of chain complexes parametrized by a finite simplicial complex $K$ forms a category with chain duality. This fact, never fully proven in the original reference (Ranicki, 1992), is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality. Our paper also gives a new, conceptual, and geometric treatment of chain duality on $K$-based chain complexes.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135265680","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: 1
Characterizations of circle homeomorphisms of different regularities in the universal Teichmüller space 普适teichmller空间中不同规律圆同胚的刻画
EMS Surveys in Mathematical Sciences Pub Date : 2023-10-24 DOI: 10.4171/emss/60
Jun Hu
{"title":"Characterizations of circle homeomorphisms of different regularities in the universal Teichmüller space","authors":"Jun Hu","doi":"10.4171/emss/60","DOIUrl":"https://doi.org/10.4171/emss/60","url":null,"abstract":"In this survey, we first give a summary of characterizations of circle homeomorphisms of different regularities (quasisymmetric, symmetric, or $C^{1+alpha}$) in terms of Beurling–Ahlfors extension, Douady–Earle extension, and Thurston's earthquake representation of an orientation-preserving circle homeomorphism. Then we provide a brief account of characterizations of the elements of the tangent spaces of these sub-Teichmüller spaces at the base point in the universal Teichmüuller space. We also investigate the regularity of the Beurling–Ahlfors extension $BA(h)$ of a $C^{1+mathrm{Zygmund}}$ orientation-preserving diffeomorphism $h$ of the real line, and show that the Beltrami coefficient $mu (BA(h))(x+iy)$ vanishes as $O(y)$ uniformly on $x$ near the boundary of the upper half plane if and only if $h$ is $C^{1+mathrmtarted with any homeomorphism of the real line that is a lifting map of an orientation-preserving circle homeomorphism.{Lipschitz}}$. Finally, we show this criterion is indeed true when $h$ is started with any homeomorphism of the real line that is a lifting map of an orientation-preserving circle homeomorphism.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"11 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266286","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
Controlled Mather–Thurston theorems 受控Mather-Thurston定理
EMS Surveys in Mathematical Sciences Pub Date : 2023-10-24 DOI: 10.4171/emss/63
Michael Freedman
{"title":"Controlled Mather–Thurston theorems","authors":"Michael Freedman","doi":"10.4171/emss/63","DOIUrl":"https://doi.org/10.4171/emss/63","url":null,"abstract":"Classical results of Milnor, Wood, Mather, and Thurston produce flat connections in surprising places. The Milnor–Wood inequality is for circle bundles over surfaces, whereas the Mather–Thurston theorem is about cobording general manifold bundles to ones admitting a flat connection. The surprise comes from the close encounter with obstructions from Chern–Weil theory and other smooth obstructions such as the Bott classes and the Godbillion–Vey invariant. Contradiction is avoided because the structure groups for the positive results are larger than required for the obstructions, e.g., $operatorname{PSL}(2,mathbb{R})$ versus $operatorname{U}(1)$ in the former case and $C^1$ versus $C^2$ in the latter. This paper adds two types of control strengthening the positive results: In many cases we are able to (1) refine the Mather–Thurston cobordism to a semi-$s$-cobordism (ssc), and (2) provide detail about how, and to what extent, transition functions must wander from an initial, small, structure group into a larger one. The motivation is to lay mathematical foundations for a physical program. The philosophy is that living in the IR we cannot expect to know, for a given bundle, if it has curvature or is flat, because we cannot resolve the fine scale topology which may be present in the base, introduced by an ssc, nor minute symmetry violating distortions of the fiber. Small scale, UV, “distortions“ of the base topology and structure group allow flat connections to simulate curvature at larger scales. The goal is to find a duality under which curvature terms, such as Maxwell's $F wedge F^ast$ and Hilbert's $int R, dmathrm{vol}$ are replaced by an action which measures such “distortions“. In this view, curvature results from renormalizing a discrete, group theoretic, structure.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":"BME-30 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218337","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: 5
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