Smooth (non)rigidity of cusp-decomposable manifolds

Details Smooth (non)rigidity of cusp-decomposable manifolds Smooth (non)rigidity of cusp-decomposable manifolds

2009-07-22

arxiv.org/abs/0907.3755v3

Mathematics

Geometric Topology

13 pages, 1 figure. Accepted for publication in Comment. Math. Helv. arXiv admin note: substantial overlap with arXiv:1105.520

Scientific paper

We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume, locally symmetric, negatively curved manifolds with cusps. We prove that the group of outer automorphisms of the fundamental group of such a manifold is an extension of an abelian group by a finite group. Elements of the abelian group are induced by diffeomorphisms that are analogous to Dehn twists in surface topology. We also prove that the outer automophism group can be realized by a group of diffeomorphisms of the manifold.

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