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Titlebook: Lectures on Functor Homology; Vincent Franjou,Antoine Touzé Book 2015 Springer International Publishing Switzerland 2015 category theory.f

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发表于 2025-3-21 19:47:10 | 显示全部楼层 |阅读模式
书目名称Lectures on Functor Homology
编辑Vincent Franjou,Antoine Touzé
视频videohttp://file.papertrans.cn/584/583514/583514.mp4
概述Explores common structures in different fields of homological algebra: homology of classical groups, rational cohomology of algebraic groups, and algebraic topology.Serves as an introduction to homolo
丛书名称Progress in Mathematics
图书封面Titlebook: Lectures on Functor Homology;  Vincent Franjou,Antoine Touzé Book 2015 Springer International Publishing Switzerland 2015 category theory.f
描述.This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems..In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results..The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schu
出版日期Book 2015
关键词category theory; functor homology; groups; representation theory; topological invariants
版次1
doihttps://doi.org/10.1007/978-3-319-21305-7
isbn_softcover978-3-319-79333-7
isbn_ebook978-3-319-21305-7Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer International Publishing Switzerland 2015
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发表于 2025-3-21 21:24:55 | 显示全部楼层
发表于 2025-3-22 00:58:27 | 显示全部楼层
,Homologie stable des groupes à coefficients polynomiaux,e colimit of the homology of a nice sequence of groups, such as the symmetric groups or as the general linear groups over a fixed ring. The lectures’ aim is to express stable homology with twisted coefficients using stable homology with untwisted coefficients and functor homology.
发表于 2025-3-22 06:00:41 | 显示全部楼层
Prerequisites of Homological Algebra,im of Sections 2 and 3 is to give a unified presentation of the various homology theories appearing in the book. In particular, we try to underline the links, the similarities and the differences between them. Section 4 is an introduction to spectral sequences, a technical tool which is used in all the other chapters.
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发表于 2025-3-22 16:21:40 | 显示全部楼层
978-3-319-79333-7Springer International Publishing Switzerland 2015
发表于 2025-3-22 19:58:40 | 显示全部楼层
Lectures on Functor Homology978-3-319-21305-7Series ISSN 0743-1643 Series E-ISSN 2296-505X
发表于 2025-3-23 00:00:48 | 显示全部楼层
Polynomial Functors and Homotopy Theory,We develop methods for proving that certain extensions of polynomial functors do not split naturally. As an application we give a functorial description of the third and the fourth stable homotopy groups of the classifying spaces of free abelian groups.
发表于 2025-3-23 02:40:31 | 显示全部楼层
Introduction,is shorthand for homological algebra in functor categories, a topic that potentially covers a large field of interests. The series presented three different fields where functor homology has recently played a significant role. For each of these applications, the functorial viewpoint provides both in
发表于 2025-3-23 06:06:48 | 显示全部楼层
,Homologie stable des groupes à coefficients polynomiaux,e colimit of the homology of a nice sequence of groups, such as the symmetric groups or as the general linear groups over a fixed ring. The lectures’ aim is to express stable homology with twisted coefficients using stable homology with untwisted coefficients and functor homology.
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