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

 

The Hasse invariant of a vector bundle


Author: Richard R. Patterson
Journal: Trans. Amer. Math. Soc. 150 (1970), 425-443
MSC: Primary 55.50; Secondary 16.00
MathSciNet review: 0268893
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Abstract: The object of this work is to define, by analogy with algebra, the Witt group and the graded Brauer group of a topological space $ X$. A homomorphism is defined between them analogous to the generalized Hasse invariant. Upon evaluation, the Witt group is seen to be $ \tilde KO(X)$, the graded Brauer group $ 1 + {H^1}(X;{Z_2}) + {H^2}(X;{Z_2})$ with truncated cup product multiplication, while the homomorphism is given by Stiefel-Whitney classes: $ 1 + {w_1} + {w_2}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0268893-4
PII: S 0002-9947(1970)0268893-4
Keywords: Vector bundles, Witt group, graded Brauer group, Hasse invariant, Clifford bundles
Article copyright: © Copyright 1970 American Mathematical Society