#### Geometry & Topology, Vol. 9 (2005)
Paper no. 26, pages 1147--1185.

## Geometry of pseudocharacters

### Jason Fox Manning

**Abstract**.
If G is a group, a pseudocharacter f: G-->R is a function which is
"almost" a homomorphism. 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.
**Keywords**.
Pseudocharacter, quasi-action, tree, bounded cohomology

**AMS subject classification**.
Primary: 57M07.
Secondary: 05C05, 20J06.

**E-print:** `arXiv:math.GR/0303380`

**DOI:** 10.2140/gt.2005.9.1147

Submitted to GT on 22 August 2003.
(Revised 9 March 2005.)
Paper accepted 8 June 2005.
Paper published 14 June 2005.

Notes on file formats
Jason Fox Manning

Mathematics 253--37, California Institute of Technology

Pasadena, CA 91125, USA

Email: manning@caltech.edu

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**