Algebraic and Geometric Topology 3 (2003), paper no. 12, pages 335-398.

A criterion for homeomorphism between closed Haken manifolds

Pierre Derbez

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.

Keywords. Haken manifold, Seifert fibered space, hyperbolic manifold, homology equivalence, finite covering, Gromov simplicial volume

AMS subject classification. Primary: 57M50. Secondary: 51H20.

DOI: 10.2140/agt.2003.3.335

E-print: arXiv:math.GT/0304076

Submitted: 18 April 2002. (Revised: 5 February 2003.) Accepted: 12 March 2003. Published: 21 March 2003.

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Pierre Derbez
Laboratoire de Topologie, UMR 5584 du CNRS
Universite de Bourgogne, 9, avenue Alain Savary - BP 47870
21078 Dijon CEDEX - France

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