English

Examples of extended geometrically finite representations

Geometric Topology 2023-12-01 v1 Group Theory

Abstract

This is the second of a pair of papers on extended geometrically finite (EGF) representations, which were originally posted as a single article under the title "An extended definition of Anosov representation for relatively hyperbolic groups." In this paper, we prove that the holonomy representation of a projectively convex cocompact manifold with relatively hyperbolic fundamental group is always an EGF representation. We also prove that EGF representations arise as holonomy representations of convex projective manifolds with generalized cusps and as compositions of projectively convex cocompact representations with symmetric representations of SL(d, R). We additionally show that any small deformation of a representation of the latter form is still EGF.

Keywords

Cite

@article{arxiv.2311.18653,
  title  = {Examples of extended geometrically finite representations},
  author = {Theodore Weisman},
  journal= {arXiv preprint arXiv:2311.18653},
  year   = {2023}
}

Comments

35 pages. The contents of this paper can still be found in earlier versions of the prequel arXiv:2205.07183

R2 v1 2026-06-28T13:37:09.737Z