Geometry & Topology

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.

Article information

Source
Geom. Topol., Volume 9, Number 2 (2005), 1147-1185.

Dates
Revised: 9 March 2005
Accepted: 8 June 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799613

Digital Object Identifier
doi:10.2140/gt.2005.9.1147

Mathematical Reviews number (MathSciNet)
MR2174263

Zentralblatt MATH identifier
1083.20038

Subjects
Primary: 57M07: Topological methods in group theory
Secondary: 05C05: Trees 20J06: Cohomology of groups

Citation

Manning, Jason Fox. Geometry of pseudocharacters. Geom. Topol. 9 (2005), no. 2, 1147--1185. doi:10.2140/gt.2005.9.1147. https://projecteuclid.org/euclid.gt/1513799613

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