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Transactions of the American Mathematical Society

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



A homotopy invariance theorem in coarse cohomology and $ K$-theory

Authors: Nigel Higson and John Roe
Journal: Trans. Amer. Math. Soc. 345 (1994), 347-365
MSC: Primary 19K56; Secondary 46L80, 55N99, 58G12
MathSciNet review: 1243611
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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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Article copyright: © Copyright 1994 American Mathematical Society