Geometry of pseudocharacters

Manning, Jason Fox¹

¹ Mathematics 253–37, California Institute of Technology, Pasadena, California 91125, USA

Geometry & topology, Tome 9 (2005) no. 2, pp. 1147-1185.

Résumé

If $G$ is a group, a pseudocharacter $f:G\to ℝ$ 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.

Détail

DOI : 10.2140/gt.2005.9.1147

Keywords: pseudocharacter, quasi-action, tree, bounded cohomology

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