Stability properties of multiplicative representations of free groups
Abstract
We extend the construction of multiplicative representations for a free group G introduced by Kuhn and Steger (Isr. J., (144) 2004) in such a way that the new class Mult(G) so defined is stable under taking the finite direct sum, under changes of generators (and hence is Aut(G)-invariant), under restriction to and induction from a subgroup of finite index. The main tool is the detailed study of the properties of the action of a free group on its Cayley graph with respect to a change of generators, as well as the relative properties of the action of a subgroup of finite index after the choice of a "nice" fundamental domain. These stability properties of Mult(G) are essential in the construction of a new class of representations for a virtually free group (Iozzi-Kuhn-Steger, arXiv:1112.4709v1)
Cite
@article{arxiv.1204.0942,
title = {Stability properties of multiplicative representations of free groups},
author = {Alessandra Iozzi and M. Gabriella Kuhn and Tim Steger},
journal= {arXiv preprint arXiv:1204.0942},
year = {2012}
}