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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The Hasse invariant of a vector bundle
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by Richard R. Patterson PDF
Trans. Amer. Math. Soc. 150 (1970), 425-443 Request permission

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
  • © Copyright 1970 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 150 (1970), 425-443
  • MSC: Primary 55.50; Secondary 16.00
  • DOI: https://doi.org/10.1090/S0002-9947-1970-0268893-4
  • MathSciNet review: 0268893