Reconstructing simplicial group actions

Abstract

This talk will describe algorithms which compress and reconstruct finite symmetric simplicial complexes. These algorithms are derived from generalisations (by Bridson-Haefliger, Carbone-Rips, and Corson, among others) of the classical Bass-Serre theory for reconstructing group actions on trees. The compression algorithm takes in a finite simplicial complex along with a subgroup G of its automorphism group, and outputs a complex of groups. The reconstruction algorithm inverts the first by using the overlaid algebraic data to correctly unfold the complex of groups so that the simplicial complex is recovered up to G-equivariant isomorphism. This talk is based on joint work with Lisa Carbone and Vidit Nanda.