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

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.