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Homotopy invariance of higher signatures and 3 -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

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...

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