Convex cocompactness in pseudo-Riemannian hyperbolic spaces
Abstract
Anosov representations of word hyperbolic groups into higher-rank semisimple Lie groups are representations with finite kernel and discrete image that have strong analogies with convex cocompact representations into rank-one Lie groups. However, the most naive analogy fails: generically, Anosov representations do not act properly and cocompactly on a convex set in the associated Riemannian symmetric space. We study representations into projective indefinite orthogonal groups PO(p,q) by considering their action on the associated pseudo-Riemannian hyperbolic space H^{p,q-1} in place of the Riemannian symmetric space. Following work of Barbot and Mérigot in anti-de Sitter geometry, we find an intimate connection between Anosov representations and the natural notion of convex cocompactness in this setting.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2017
- DOI:
- 10.48550/arXiv.1701.09136
- arXiv:
- arXiv:1701.09136
- Bibcode:
- 2017arXiv170109136D
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Group Theory
- E-Print:
- 46 pages, 7 figures. To appear in Geometriae Dedicata, special issue in honor of Bill Goldman's 60th birthday