Polyhedral products, flag complexes and monodromy representations

Abstract

This article presents a machinery based on polyhedral products that produces faithful representations of graph products of finite groups and direct products of finite groups into automorphisms of free groups $\mathrm{Aut}({\mathrm{F}}_{\mathrm{n}})$ and outer automorphisms of free groups $\mathrm{Out}({\mathrm{F}}_{\mathrm{n}})$, respectively, as well as faithful representations of products of finite groups into the linear groups $\mathrm{SL}(\mathrm{n},\mathbb{Z})$ and $\mathrm{GL}(\mathrm{n},\mathbb{Z})$. These faithful representations are realized as monodromy representations.

20 pages