Groups acting on hyperbolic spaces—a survey

  • Mladen Bestvina

    Department of Mathematics, University of Utah, 155 S 1400 E, RM 233, Salt Lake City, UT 84112, USA
Groups acting on hyperbolic spaces—a survey cover
Download Chapter PDF

This book chapter is published open access.


This is a (very subjective) survey paper for nonspecialists, covering group actions on Gromov hyperbolic spaces. The first section is about hyperbolic groups themselves, while the rest of the paper focuses on mapping class groups and , and the way to understand their large scale geometry using their actions on various hyperbolic spaces constructed using projection complexes. This understanding for significantly lags behind that of mapping class groups, and the paper ends with a few open questions.