A notion of geometric complexity and its application to topological rigidity Academic Article uri icon

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. © 2011 Springer-Verlag.

author list (cited authors)

  • Guentner, E., Tessera, R., & Yu, G.

citation count

  • 45

complete list of authors

  • Guentner, Erik||Tessera, Romain||Yu, Guoliang

publication date

  • December 2011