A criterion for homeomorphism between closed Haken manifolds

Derbez, Pierre¹

¹Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, 9, avenue Alain Savary, BP 47870, 21078 Dijon CEDEX, France

Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 335-398

Résumé

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.

Détail

DOI : 10.2140/agt.2003.3.335

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

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