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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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