Actions on products of CAT(-1) spaces

2018/09/21 by García, Teresa, Porti, Joan
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1809.08189

Abstract

We show that for X a proper CAT(-1) space there is a maximal open subset of the horofunction compactification of X× X with respect to the maximum metric that compactifies the diagonal action of an infinite quasi-convex group of the isometries of X. We also consider the product action of two quasi-convex representations of an infinite hyperbolic group on the product of two different proper CAT(-1) spaces.

Related

• Compactification of a diagonal action on the product of CAT(-1) spaces
• Central extensions and proper actions on products of hyperbolic spaces
• Constructing metric spaces from systems of walls
• Rigidity of convex co-compact diagonal actions
• Detecting product splittings of CAT(0) spaces