A fixed-point property of finitely generated groups and an energy of equivariant maps

Abstract

The purpose of this article is to present sufficient conditions for an isometric action of a finitely generated group to have a fixed point in terms of an energy of equivariant maps (Proposition 2.1 and Theorem 3.1), which turn out to be useful in proving that groups with fixed-point property form a large family in the set of finitely presented groups. Most of the results are included in [7] and [8].