Convex cocompactness in pseudo-Riemannian hyperbolic spaces

Jeffrey Danciger; François Guéritaud; Fanny Kassel

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arXiv · 1701.09136

Convex cocompactness in pseudo-Riemannian hyperbolic spaces

Jeffrey Danciger·François Guéritaud·Fanny Kassel

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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.

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BibTeX RIS

Jeffrey Danciger, François Guéritaud, Fanny Kassel. 2017-09-28. Convex cocompactness in pseudo-Riemannian hyperbolic spaces. https://arxiv.org/abs/1701.09136

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