Volume 9, issue 2 (2005)

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Geometry of pseudocharacters

Jason Fox Manning

Geometry & Topology 9 (2005) 1147–1185
 arXiv: math.GR/0303380
Abstract

If $G$ is a group, a pseudocharacter $f:\phantom{\rule{0.3em}{0ex}}G\to ℝ$ 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
Mathematical Subject Classification 2000
Primary: 57M07
Secondary: 05C05, 20J06
Publication
Revised: 9 March 2005
Accepted: 8 June 2005
Published: 14 June 2005
Proposed: Martin Bridson
Seconded: Dieter Kotschick, Benson Farb
Authors
 Jason Fox Manning Mathematics 253–37 California Institute of Technology Pasadena California 91125 USA