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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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Orthogonal calculus
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by Michael Weiss PDF
Trans. Amer. Math. Soc. 347 (1995), 3743-3796 Request permission

Erratum: Trans. Amer. Math. Soc. 350 (1998), 851-855.

Abstract:

Orthogonal calculus is a calculus of functors, similar to Goodwillie’s calculus. The functors in question take finite dimensional real vector spaces (with an inner product) to pointed spaces. Prime example: $F(V) = BO(V)$, where $O(V)$ is the orthogonal group of $V$. In this example, and in general, first derivatives in the orthogonal calculus reproduce and generalize much of the theory of Stiefel-Whitney classes. Similarly, second derivatives in the orthogonal calculus reproduce and generalize much of the theory of Pontryagin classes.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 3743-3796
  • MSC: Primary 55P65; Secondary 55R40, 55S45, 55U40, 57R20
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1321590-3
  • MathSciNet review: 1321590