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

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.

arXiv commentAn error was found in the proof of the main theorem in the previous version. The argument has been revised accordingly, and the present version proves a weaker form of the main theorem