A homotopy invariance theorem in coarse cohomology and $K$-theory
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- by Nigel Higson and John Roe
- Trans. Amer. Math. Soc. 345 (1994), 347-365
- DOI: https://doi.org/10.1090/S0002-9947-1994-1243611-8
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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.References
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Bibliographic 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