A criterion for homeomorphism between closed Haken manifolds

Abstract

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-12.abs.html