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A criterion for homeomorphism between closed Haken manifolds.

Derbez, Pierre — 2003

Algebraic & Geometric Topology

Local rigidity of aspherical three-manifolds

Pierre Derbez — 2012

Annales de l’institut Fourier

In this paper we construct, for each aspherical oriented $3$ -manifold $M$ , a $2$ -dimensional class in the $l_{1}$ -homology of $M$ whose norm combined with the Gromov simplicial volume of $M$ gives a characterization of those nonzero degree maps from $M$ to $N$ which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of $M$ and $N$ .

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