Clifford module invariants of spin bundles

Allard, Jacques; Bahri, Anthony

doi:10.1090/S0002-9947-1982-0670927-8

Clifford module invariants of spin bundles
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by Jacques Allard and Anthony Bahri PDF

Trans. Amer. Math. Soc. 274 (1982), 193-202 Request permission

Abstract:

In this paper, we study $KO$-theory invariants of Spin bundles obtained by the $\alpha$-construction from Clifford module representations of the Spinor group. We begin by describing their elementary properties including various Whitney sum formulae and their relation with the $d$-invariant for vector bundles over spheres. We next observe an important difference between the two half-Spin representations and then proceed to investigate the fiber homotopy properties of the invariants. We conclude with some applications.

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