# Geometry of pseudocharacters

@article{Manning2005GeometryOP, title={Geometry of pseudocharacters}, author={Jason Fox Manning}, journal={Geometry \& Topology}, year={2005}, volume={9}, pages={1147-1185} }

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” quasi-actions on trees.

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