Volume 3, issue 1 (2003)

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A criterion for homeomorphism between closed Haken manifolds

Pierre Derbez

Algebraic & Geometric Topology 3 (2003) 335–398
 arXiv: math.GT/0304076
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 $f:\phantom{\rule{0.3em}{0ex}}{M}^{3}\to {N}^{3}$ 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
Primary: 57M50
Secondary: 51H20