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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Clifford module invariants of spin bundles


Authors: Jacques Allard and Anthony Bahri
Journal: Trans. Amer. Math. Soc. 274 (1982), 193-202
MSC: Primary 55R25; Secondary 15A66, 55R40, 57R15
MathSciNet review: 670927
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670927-8
PII: S 0002-9947(1982)0670927-8
Article copyright: © Copyright 1982 American Mathematical Society