Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups

Abstract EN

We give a short proof of the following theorem of Sang-hyun Kim: if A(Γ) is a right-angled Artin group with defining graph Γ, then A(Γ) contains a hyperbolic surface subgroup if Γ contains an induced subgraph C¯n for some n≥5, where C¯n denotes the complement graph of an n-cycle.

Furthermore, we give a new proof of Kim's cocontraction theorem.