#### 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.

Notes on file formats
Pierre Derbez

Laboratoire de Topologie, UMR 5584 du CNRS

Universite de Bourgogne, 9, avenue Alain Savary - BP 47870

21078 Dijon CEDEX - France

Email: derbez@topolog.u-bourgogne.fr

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