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arXiv · 1012.4208

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

Robert W. Bell
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Abstract

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 $\bar{C}_n$ for some $n \geq 5$, where $\bar{C}_n$ denotes the complement graph of an $n$-cycle. Furthermore, we give a new proof of Kim's co-contraction theorem.

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BibTeXRIS

Robert W. Bell. 2010-12-19. Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups. https://arxiv.org/abs/1012.4208

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