Groupes fondamentaux des varietes de dimension 3 et algebres   d'operateurs
  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). 
Pierre de la Harpe and Jean-Philippe Preaux