A homotopy invariance theorem in coarse cohomology and -theory

Authors:
Nigel Higson and John Roe

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

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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 -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 -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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DOI:
https://doi.org/10.1090/S0002-9947-1994-1243611-8

Article copyright:
© Copyright 1994
American Mathematical Society