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

 

Orthogonal calculus


Author: Michael Weiss
Journal: Trans. Amer. Math. Soc. 347 (1995), 3743-3796
MSC: Primary 55P65; Secondary 55R40, 55S45, 55U40, 57R20
Erratum: Trans. Amer. Math. Soc. 350 (1998), 851-855.
MathSciNet review: 1321590
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Abstract | References | Similar Articles | Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1321590-3
PII: S 0002-9947(1995)1321590-3
Keywords: Calculus of functors, characteristic classes
Article copyright: © Copyright 1995 American Mathematical Society