Koji Fujiwara: Quasi-cocycles on free groups to uniformly convex Banach spaces

Abstract: Let G be a group and E a normed vector space. We denote by O(E) the group of norm-preserving isomorphisms from E to E. Let f: G -> O(E) be a linear representation of G. A map F :G -> E is a cocycle if F(gg')=F(g) +f(g) F(g'). Equivalently, F gives an action of G on E by isometries with linear part f. We can define "quasi-cocycles" which correspond to quasi-actions of G on E by isometries with linear part f. In this talk we discuss quasi-cocycles on free groups for "uniformly convex" Banach spaces E. For example, ell^p(G) is uniformly convex for 1 < p < infty.