2012/04/04 by Alessandra Iozzi, Iozzi, Alessandra, M. Gabriella Kuhn +3
Mathematics · #22D10 #43A65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:22D10 #msc:43A65
paper · pdf · doi:10.48550/arxiv.1204.0942
arxiv created 2012/04/04 · openalex publication_date 2012/04/04 · arxiv updated 2012/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)