The simplicial complex of graphs of groups
Jiang, Renfang · Università del Salento · 2009
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 $Fn$ are connected by a sequence of blow ups and collapses.