A note on the homology of hyperbolic groups

Abstract

Abstract Hyperbolic groups have been studied in various fields in mathematics. They appear in contexts as diverse as geometric group theory, function theory (as Fuchsian groups) and algebraic topology (as fundamental groups of compact hyperbolic surfaces). Hyperbolic groups possess geometrical properties well suited for the study of homological finiteness conditions. In this paper we will prove some of these results via free resolutions obtained from the Rips-complex.