Integral invariants and cohomology of \(B\text{Spin}(n)\)
type: Item
instance of: scholarly article
title: Integral invariants and cohomology of \(B\text{Spin}(n)\)
zbMATH Open document ID: 0846.55013
DOI: 10.1016/0040-9383(94)E0019-G
author: Jay A. Wood
author: David Benson
published in: Topology
publication date: 1996-09-25T00:00:00Z
review text: Let \(\text{Spin} (n)\) be the spinor group and \(B \text{Spin} (n)\) its classifying space. The authors describe the integral cohomology \(H^* (B \text{Spin} (n), \mathbb{Z})\) as a pullback. The precise generators for \[ H^* (B \text{Spin} (n), \mathbb{Z})/ \text{torsion} \] and the form of their relations are given, but no explicit generators and relations for \(H^* (B \text{Spin} (n), \mathbb{Z})\) itself. In the stable case the groups \(H^* (B \text{Spin}, \mathbb{Z})\) and \(H^* (B \text{Spin}, \mathbb{Z}/2)\) have been calculated by \textit{E. Thomas} [Bol. Soc. Mat. Mexicana, II. Ser. 7, 57-69 (1962; Zbl 0124.16401)].
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 57T10
zbMATH DE Number: 722017
zbMATH Keywords: integral cohomology
zbMATH Keywords: Bockstein cohomology
zbMATH Keywords: classifying space
zbMATH Keywords: compact Lie group
zbMATH Keywords: Euler class
zbMATH Keywords: Pontrjagin class
zbMATH Keywords: spinor group
zbMATH Keywords: Weyl group
reviewed by: Marek Golasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 722017