The simplicial complex of graphs of groups

Abstract

Graphs of groups with length functions are defined to parametrize simplicial Gtrees. Collapses of graphs of groups define a partial order and a simplicial structure on the set of simplicial G-trees. There is a bijective continuous map from this simplicial complex to the space of non-abelian simplicial projective translation length functions of G. Any two small splittings of $F_n$ are connected by a sequence of blow ups and collapses.