2023/02/09 by Nir Lazarovich, Lazarovich, Nir · 1 citation
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2302.04484
We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a graph to the minimal number of cells in a simplicial classifying space for the group. As a corollary we prove that any two isomorphic finite-index subgroups of a non-elementary hyperbolic group have the same index.