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 : G 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
References
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Publication
Received: 22 August 2003
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