On établit pour les centralisateurs dans une PD(3) paire des résultats analogues à ceux connus pour les centralisateurs dans un groupe fondamental de variété de dimension 3. Comme dans le cas des groupes fondamentaux de variétés de dimension 3, la preuve de ces résultats repose sur une décomposition JSJ pour les PD(3) paires obtenue à l'aide de la théorie des voisinages algébriques réguliers de Scott et Swarup.
We prove for centralizers in PD(3) pairs some results known for centralizers in 3-manifold fundamental groups. As in the 3-manifold case, the main ingredient of the proofs is a JSJ decomposition for PD(3) pairs obtained by mean of the Scott and Swarup regular neighborood theory.
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@article{CRMATH_2004__338_12_935_0,
author = {Fabrice Castel},
title = {Centralisateurs dans les groupes \`a dualit\'e de {Poincar\'e} de dimension 3},
journal = {Comptes Rendus. Math\'ematique},
pages = {935--940},
publisher = {Elsevier},
volume = {338},
number = {12},
year = {2004},
doi = {10.1016/j.crma.2004.03.037},
language = {fr},
}
Fabrice Castel. Centralisateurs dans les groupes à dualité de Poincaré de dimension 3. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 935-940. doi : 10.1016/j.crma.2004.03.037. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.037/
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