Cohomologie des groupes et des espaces de transformation. (Group cohomology and transformation spaces)
type: Item
instance of: scholarly article
title: Cohomologie des groupes et des espaces de transformation. (Group cohomology and transformation spaces)
zbMATH Open document ID: 0634.55004
DOI: 10.1016/0021-8693(88)90094-4
author: Bernard Magneron
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The concept of a locally trivial extension of a transformation space (G,X) by a G-module A in a suitable category of topological spaces with superstructure (discrete, differential, algebraic,...) is introduced. This extends the notion of topologically locally trivial group extensions. Then, using group and equivariant Čech cohomology, a general cohomology theory for these extensions is developed. This can be used, for instance, to study their functorial or their reduction properties. This theory is applied, in another paper [ibid. 112, No.2, 349-369 (1988; see the following review Zbl 0634.55005)], to obtain cohomological descriptions of the varieties of pure spinors and of the spin groups.
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55N05
Mathematics Subject Classification ID: 57S99
Mathematics Subject Classification ID: 20J99
zbMATH DE Number: 4032601
zbMATH Keywords: locally trivial extension of a transformation space by a G-module
zbMATH Keywords: group cohomology
zbMATH Keywords: equivariant Čech cohomology
zbMATH Keywords: general cohomology theory
zbMATH Keywords: reduction
zbMATH Keywords: varieties of pure spinors and of the spin groups
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90094-4
OpenAlex ID: W2021137717
cites work: Sur un théorème d'intégralité de B. Kostant
cites work: Q3915179
cites work: Q5600061
cites work: Sur quelques points d'algèbre homologique
cites work: The Weil representation, Maslov index and theta series
cites work: Q3668485
cites work: Spineurs symplectiques purs et indice de Maslov de plans lagrangiens positifs
cites work: Q5340160
cites work: Algebraic Cohomology of Topological Groups
cites work: Q5605675
cites work: Q3963102
cites work: Questions de rationalité des diviseurs en géométrie algébrique
cites work: Q3313974
cites work: Q4744461
cites work: Q4120673
description: scientific article; zbMATH DE number 4032601