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Geometry of pseudocharacters

Manning, Jason Fox (2005) Geometry of pseudocharacters. Geometry and Topology, 9 (26). pp. 1147-1185. ISSN 1465-3060. doi:10.2140/gt.2005.9.1147.

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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.

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Additional Information:Submitted to GT on 22 August 2003. (Revised 9 March 2005.) Paper accepted 8 June 2005. Paper published 14 June 2005. I would like to thank my PhD advisor Daryl Cooper for his guidance, support and inspiration. This work was partially supported by the NSF, and by a UCSB Graduate Division Dissertation Fellowship. Thanks also to the Oxford Mathematical Institute for hospitality while part of this work was being done, and to the referee for several useful comments.
Subject Keywords:Pseudocharacter, quasi-action, tree, bounded cohomology
Issue or Number:26
Classification Code:AMS subject classification. Primary: 57M07. Secondary: 05C05, 20J06.
Record Number:CaltechAUTHORS:MANgt05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1273
Deposited By: Archive Administrator
Deposited On:07 Jan 2006
Last Modified:08 Nov 2021 19:08

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