Local rigidity of aspherical three-manifolds

Pierre Derbez[1]

  • [1] LATP, UMR 6632, Centre de Mathématiques et d’Informatique, Technopole de Chateau-Gombert, 39, rue Frédéric Joliot-Curie - 13453 Marseille Cedex 13

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 393-416
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Derbez, Pierre. "Local rigidity of aspherical three-manifolds." Annales de l’institut Fourier 62.1 (2012): 393-416. <http://eudml.org/doc/251136>.

@article{Derbez2012,
abstract = {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 $N$.},
affiliation = {LATP, UMR 6632, Centre de Mathématiques et d’Informatique, Technopole de Chateau-Gombert, 39, rue Frédéric Joliot-Curie - 13453 Marseille Cedex 13},
author = {Derbez, Pierre},
journal = {Annales de l’institut Fourier},
keywords = {Aspherical $3$-manifolds; bounded cohomology; $l_1$-homology; non-zero degree maps; topological rigidity; aspherical 3-manifolds},
language = {eng},
number = {1},
pages = {393-416},
publisher = {Association des Annales de l’institut Fourier},
title = {Local rigidity of aspherical three-manifolds},
url = {http://eudml.org/doc/251136},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Derbez, Pierre
TI - Local rigidity of aspherical three-manifolds
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 393
EP - 416
AB - 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 $N$.
LA - eng
KW - Aspherical $3$-manifolds; bounded cohomology; $l_1$-homology; non-zero degree maps; topological rigidity; aspherical 3-manifolds
UR - http://eudml.org/doc/251136
ER -

References

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