| Affiliation: | (1) Department of Mathematics, University of Florida, PO Box 118105, 358 Little Hall, Gainesville, FL, 2611-8105, U.S.A |
| Abstract: | We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then M×ℝ n is homeomorphic to N×ℝ n , for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K. |
