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Groupes fondamentaux des variétés de dimension 3 et algèbres d'opérateurs

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Préaux, Jean-Philippe
Published in Annales de la Faculté des Sciences de Toulouse. 2007, vol. 16, no. 3, p. 561-589
Abstract We provide a geometric characterization of manifolds of dimension 3 with fundamental groups of which all conjugacy classes except 1 are infinite, namely of which the von Neumann algebras are factors of type $II_1$: they are essentially the 3-manifolds with infinite fundamental groups on which there does not exist any Seifert fibration. Otherwise said and more precisely, let $M$ be a compact connected 3-manifold and let $Gamma$ be its fundamental group, supposed to be infinite and with at least one finite conjugacy class besides 1. If $M$ is orientable, then $Gamma$ is the fundamental group of a Seifert manifold; if $M$ is not orientable, then $Gamma$ is the fundamental group of a Seifert manifold modulo $Bbb P$ in the sense of Heil and Whitten cite{HeWh--94}. We make heavy use of results on 3-manifolds, as well classical results (as can be found in the books of Hempel, Jaco, and Shalen), as more recent ones (solution of the Seifert fibred space conjecture).
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DE LA HARPE, Pierre, PRÉAUX, Jean-Philippe. Groupes fondamentaux des variétés de dimension 3 et algèbres d'opérateurs. In: Annales de la Faculté des Sciences de Toulouse, 2007, vol. 16, n° 3, p. 561-589. https://archive-ouverte.unige.ch/unige:9804

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Deposited on : 2010-07-30

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