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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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A homotopy invariance theorem in coarse cohomology and $K$-theory
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by Nigel Higson and John Roe PDF
Trans. Amer. Math. Soc. 345 (1994), 347-365 Request permission

Abstract:

We introduce a notion of homotopy which is appropriate to the coarse geometry and topology studied by the second author in [7]. We prove the homotopy invariance of coarse cohomology, and of the K-theory of the ${C^\ast }$-algebra associated to a coarse structure on a space. We apply our homotopy invariance results to show that if M is a Hadamard manifold then the inverse of the exponential map at any point 0 induces an isomorphism between the K-theory groups of the ${C^\ast }$-algebras associated to M and its tangent space at 0 (see Theorem 7.9). This result is consistent with a coarse version of the Baum-Connes conjecture.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 345 (1994), 347-365
  • MSC: Primary 19K56; Secondary 46L80, 55N99, 58G12
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1243611-8
  • MathSciNet review: 1243611