A homotopy invariance theorem in coarse cohomology and k-theory

Nigel Higson, John Roe

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8 Scopus citations

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 if-theory of the C*-algebra associated to a coarse structure on a space. We apply our homotopy invariance results to show that if Af 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*-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.

Original languageEnglish (US)
Pages (from-to)347-365
Number of pages19
JournalTransactions of the American Mathematical Society
Volume345
Issue number1
DOIs
StatePublished - Sep 1994

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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