Homotopy invariance of higher signatures and 3-manifold groups

Michel Matthey (1) , Hervé Oyono-Oyono (2) , Wolfgang Pitsch (3)

1 IGAT - Institut de Géométrie, Algèbre et Topologie
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable 3-manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients holds. The non-oriented case is also discussed.

Mots clés: Baum-Connes conjecture; JSJ decomposition; Thurston Geometrization Conjecture

Domaines: Algèbres d'opérateurs [math.OA]; K-théorie et homologie [math.KT]; Topologie géométrique [math.GT]

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch. Homotopy invariance of higher signatures and 3-manifold groups. Bulletin de la société mathématique de France, 2008, 136 (1), pp.1-25. ⟨hal-00483095⟩