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 quasiaction 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" quasiactions on trees.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2003
 arXiv:
 arXiv:math/0303380
 Bibcode:
 2003math......3380F
 Keywords:

 Mathematics  Group Theory;
 57M07;
 05C05;
 20J06
 EPrint:
 Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper26.abs.html