Geometry of pseudocharacters

Manning, Jason Fox

doi:10.2140/gt.2005.9.1147

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Geometry of pseudocharacters

Jason Fox Manning

Geometry & Topology 9 (2005) 1147–1185

DOI: 10.2140/gt.2005.9.1147

arXiv: math.GR/0303380

Abstract

If $G$ is a group, a pseudocharacter $f : G \to ℝ$ 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

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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

Volume 9, issue 2 (2005)