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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A criterion for homeomorphism between closed Haken manifolds

Pierre Derbez

Algebraic & Geometric Topology 3 (2003) 335–398

arXiv: math.GT/0304076

Abstract

In this paper we consider two connected closed Haken manifolds denoted by M3 and N3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f : M3 N3 between M3 and N3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M3 and N3 satisfying the homological hypothesis of the map f.

Keywords
Haken manifold, Seifert fibered space, hyperbolic manifold, homology equivalence, finite covering, Gromov simplicial volume
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 51H20
References
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Publication
Received: 18 April 2002
Revised: 5 February 2003
Accepted: 12 March 2003
Published: 21 March 2003
Authors
Pierre Derbez
Laboratoire de Topologie
UMR 5584 du CNRS
Université de Bourgogne
9, avenue Alain Savary
BP 47870
21078 Dijon CEDEX
France