| Authors: | Nigel Higson and John Roe |
| Title: | A homotopy invariance theorem in coarse cohomology and K-theory |
| Publication Information: | Trans. Amer. Math. Soc., 345 (1994), 347-365 |
| Abstract: | We introduce a notion of homotopy which is appropriate to the coarse geometry and topology studied by the second author. We prove the homotopy invariance of coarse cohomology, and of the K-theory of the C*-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*-algebras associated to M and its tangent space at 0. This result is consistent with a coarse version of the Baum-Connes conjecture. |