Geometry of pseudocharacters

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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper26.abs.html

References in corpus (2)

• Bounded cohomology of subgroups of mapping class groups
• Quasi-homomorphisms and stable lengths in mapping class groups

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• Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
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• Bushy pseudocharacters and group actions on quasi-trees
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