Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space

David Xu

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arXiv · 2402.12294

Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space

David Xu

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Abstract

We prove that convex-cocompact representations of finitely generated groups in the group of isometries of the infinite-dimensional hyperbolic space form an open set in the space of representations, allowing us to deform these convex-cocompact representations. We then use bending to obtain convex-cocompact representations of surface groups that are not conjugate to any exotic representation of PSL(2,R) classified by Monod and Py.

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David Xu. 2024-02-19. Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space. https://arxiv.org/abs/2402.12294

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