A criterion for homeomorphism between closed Haken manifolds

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 $f : M^{3} \to N^{3}$ 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

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

Volume 3, issue 1 (2003)

Pierre Derbez