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G&T Monographs |
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Geometry of pseudocharacters
Jason Fox Manning
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Geometry & Topology 9 (2005)
1147–1185
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Abstract
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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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Keywords
pseudocharacter, quasi-action, tree,
bounded cohomology
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Mathematical Subject Classification
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
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