On Finite domination and Poincaré duality

Abstract

The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let $\pi$ be finitely presented group. Assuming that the reduced Grothendieck group ${\tilde{K}}_0(\mathbb{Z}[\pi ])$ has a non-trivial 2-divisible element, we construct a finitely dominated Poincaré space $X$ with fundamental group $\pi$ such that $X$ is not homotopy finite. The dimension of $X$ can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening.

Final version. To appear in Homology, Homotopy and Applications

Cited by in corpus (1)

• Poincaré Complex Diagonals and the Bass trace Conjecture