Homotopy invariance of higher signatures and 3-manifold groups

2004/12/18 by Michel Matthey, Hervé Oyono‐Oyono, Hervé Oyono-Oyono +4
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.math/0412363

13 pages

arxiv created 2004/12/18 · arxiv updated 2009/12/01

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.

Citations

• �ber die Topologie des dreidimensionalen Raumes
• The Geometries of 3-Manifolds

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