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Integral invariants and cohomology of \(B\text{Spin}(n)\). (English) Zbl 0846.55013

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 E. Thomas [Bol. Soc. Mat. Mexicana, II. Ser. 7, 57-69 (1962; Zbl 0124.16401)].

MSC:

55R40 Homology of classifying spaces and characteristic classes in algebraic topology
57T10 Homology and cohomology of Lie groups

Citations:

Zbl 0124.16401
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