Séminaire de Géométrie, Groupes et Dynamique

Anders Karlsson: "Torsion groups of subexponential growth cannot act on finite-dimensional CAT(0)-spaces without a fixed point"

435 (UMPA)



In a recent paper with H. Izeki, we show that finitely generated torsion (or simple) groups of subexponential growth must have a global fixed point whenever they act by isometry on a finite dimensional complete CAT(0)-space.  Examples include the Grigorchuk groups and certain groups constructed by Nekrashevych. It is known to be false if the condition of finite dimension is removed. The method of proof is inspired by previous work by Bourdon and by Izeki. It uses ultralimits of actions, equivariant harmonic maps, subharmonic functions, horofunctions and random walks.