Clifford Module Invariants of Spin Bundles

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 vecto...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1982, Vol.274 (1), p.193-202
Main Authors: Allard, Jacques, Bahri, Anthony
Format: Article
Language:English
Subjects:
Algebraic topology
Homomorphisms
Lie groups
Mathematical theorems
Mathematical triviality
Mathematical vectors
Spinor groups
Tangents
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Summary: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.
ISSN:0002-9947
DOI:10.1090/S0002-9947-1982-0670927-8