Local rigidity of aspherical three-manifolds
Annales de l'Institut Fourier, Volume 62 (2012) no. 1, p. 393-416
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.
Dans ce papier nous construisons, pour chaque variété de dimension trois close orientable et asphérique M, une classe d’homologie l 1 de dimension deux dans M dont la norme permet avec le volume simplicial de M de caractériser les applications de degré non-nul de M dans N qui sont homotopes à un revêtement. Comme conséquence, nous donnons un critère d’homéomorphisme pour les applications de degré un en terme d’isométries entre les groupes de cohomologie bornée de M et N.
DOI : https://doi.org/10.5802/aif.2708
Classification:  57M50,  51H20
Keywords: Aspherical 3-manifolds, bounded cohomology, l 1 -homology, non-zero degree maps, topological rigidity.
@article{AIF_2012__62_1_393_0,
     author = {Derbez, Pierre},
     title = {Local rigidity of aspherical three-manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {1},
     year = {2012},
     pages = {393-416},
     doi = {10.5802/aif.2708},
     zbl = {1255.57016},
     mrnumber = {2986274},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2012__62_1_393_0}
}
Local rigidity of aspherical three-manifolds. Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 393-416. doi : 10.5802/aif.2708. https://aif.centre-mersenne.org/item/AIF_2012__62_1_393_0/

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