Homotopy invariance of higher signatures and 3-manifold groups

Michel Matthey; Hervé Oyono-Oyono; Wolfgang Pitsch

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Homotopy invariance of higher signatures and 3-manifold groups

Michel Matthey·Hervé Oyono-Oyono·Wolfgang Pitsch

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Abstract

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.

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BibTeX RIS

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch. 2004-12-18. Homotopy invariance of higher signatures and 3-manifold groups. https://arxiv.org/abs/math/0412363

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