[Rigidité topologique des variétés asphériques de dimension trois]
Dans ce papier nous construisons, pour chaque variété de dimension trois close orientable et asphérique , une classe d’homologie de dimension deux dans dont la norme permet avec le volume simplicial de de caractériser les applications de degré non-nul de dans 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 et .
In this paper we construct, for each aspherical oriented -manifold , a -dimensional class in the -homology of whose norm combined with the Gromov simplicial volume of gives a characterization of those nonzero degree maps from to 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 and .
Keywords: Aspherical $3$-manifolds, bounded cohomology, $l_1$-homology, non-zero degree maps, topological rigidity.
Mot clés : variétés asphériques de dimension trois, cohomologie bornée, homologie $l_1$, applications de degré non-nul, rigidité topologique.
Derbez, Pierre 1
@article{AIF_2012__62_1_393_0,
author = {Derbez, Pierre},
title = {Local rigidity of aspherical three-manifolds},
journal = {Annales de l'Institut Fourier},
pages = {393--416},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {62},
number = {1},
year = {2012},
doi = {10.5802/aif.2708},
mrnumber = {2986274},
zbl = {1255.57016},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2708/}
}
TY - JOUR AU - Derbez, Pierre TI - Local rigidity of aspherical three-manifolds JO - Annales de l'Institut Fourier PY - 2012 SP - 393 EP - 416 VL - 62 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2708/ DO - 10.5802/aif.2708 LA - en ID - AIF_2012__62_1_393_0 ER -
%0 Journal Article %A Derbez, Pierre %T Local rigidity of aspherical three-manifolds %J Annales de l'Institut Fourier %D 2012 %P 393-416 %V 62 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2708/ %R 10.5802/aif.2708 %G en %F AIF_2012__62_1_393_0
Derbez, Pierre. Local rigidity of aspherical three-manifolds. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 393-416. doi : 10.5802/aif.2708. https://aif.centre-mersenne.org/articles/10.5802/aif.2708/
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