Homotopy invariance of higher signatures and $3$-manifold groups

Michel Matthey、Hervé Oyono‐Oyono、Wolfgang Pitsch

2008Bulletin de la Société mathématique de FranceMathematics被引 11开放获取

摘要

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.

引用本文（GB/T 7714）

Michel Matthey, Hervé Oyono‐Oyono, Wolfgang Pitsch. Homotopy invariance of higher signatures and $3$-manifold groups[J]. Bulletin de la Société mathématique de France, 2008.

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DOI：https://doi.org/10.24033/bsmf.2547

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