Integral invariants and cohomology of \(B\text{Spin}(n)\)
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)].
scientific article; zbMATH DE number 722017