Pseudocharacters

Geometry and Topology, Volume 9 (2005) Paper no. 26, pages 1147--1185


Geometry of pseudocharacters

Author(s):
Jason Fox Manning

Abstract:

If G is a group, a pseudocharacter f: G-->R is a function which is
"almost" a homomorphism. [in a coarse-geometric sense: JR]
If G admits a nontrivial pseudocharacter f,
we define the space of ends of G relative to f and show that if the
space of ends is complicated enough, then G contains a nonabelian free
group. We also construct a quasi-action by G on a tree whose space of
ends contains the space of ends of G relative to f. This construction
gives rise to examples of "exotic" quasi-actions on trees.