Actions of certain arithmetic groups on Gromov hyperbolic spaces

Abstract

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

v1: 23 pages, 4 figures. v2: 24 pages, 4 figures. Fixed a bad typo in Claim 3.3 and made some other small changes. v3: A few small clarifications. To appear in AGT

References in corpus (4)

• Bounded cohomology of subgroups of mapping class groups
• Superrigidity for irreducible lattices and geometric splitting
• Geometry of pseudocharacters
• Quasi-homomorphisms and stable lengths in mapping class groups

Cited by in corpus (1)

• Hyperbolic structures on groups