Dimensions of CAT(0) E(G) and \underline{E}(G) spaces

Noel Brady

Abstract: (Joint work with John Crisp, Universite de Bourgogne) Let G be a discrete group. A contractible, free G-CW complex X is said to be a model for E(G). A proper G-CW complex X is a model for \underline{E}(G) if the fixed point set X^H is contractible for all finite subgroups H < G. We define nonpositively curved (CAT(0) and CAT(-1)) versions of the E(G) and \underline{E}(G) spaces above by adding the requirement that G should act by semisimple isometries. We compare minimal dimensions of the E(G) and \underline{E}(G) spaces and their nonpositively curved versions for certain families of Artin groups, and quotients of planar hyperbolic tiling groups.

created Thu May 18 14:48:08 PDT 2000