Seminario teoría de grupos UAM-ICMAT
"Counting with the falsification by fellow traveler property"
11:30, Aula 520, UAM
Abstract: The falsification by fellow traveler property was introduced by Walter Neumann and Mike Shapiro following ideas of Cannon in their study of Cayley graphs of geometrically finite hyperbolic groups. Among other things, they showed that it implies that the growth of a group is rational.
In this talk will revise this property and we will use it in the context of locally finite vertex-transitive graphs to count 'convex' subgraphs, generalizing results of Epstein, Iano-Fletcher and Zwick, and of Calegari and Fujiwara. As a consequence, we get that if G is a non-elementary hyperbolic group, then there is a lower bound on the growth rate of its Schreier graphs with respect to infinite index quasi-convex subgroups.