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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. http://resolver.caltech.edu/CaltechAUTHORS:MANgt05

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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.


Item Type:Article
Additional Information:Submitted to GT on 22 August 2003. (Revised 9 March 2005.) Paper accepted 8 June 2005. Paper published 14 June 2005. Acknowledgements 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. E-print: arXiv:math.GR/0303380
Subject Keywords:Pseudocharacter, quasi-action, tree, bounded cohomology
Record Number:CaltechAUTHORS:MANgt05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MANgt05
Alternative URL:http://dx.doi.org/10.2140/gt.2005.9.1147
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1273
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:07 Jan 2006
Last Modified:26 Dec 2012 08:43

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