Topological superrigidty

Description/Abstract

The geometric superrigidity theorem states broadly, that for Gamma in a wide class of uniform lattices, a non-constant Gamma-equivariant harmonic map is, up to rescaling, a totally geodesic embedding. In this paper we propose a topological analogue; applying surgery techniques we prove for n=2k>5 that every codimension-1 \pi1-injective continuous map from a certain type of n-manifold into a closed, aspherical orientable smooth (n+1)-manifold factors, up to homotopy, as a finite cover of an embedding.