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

2010/12/19 by Robert W. Bell, Bell, Robert W. · 1 citation
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1012.4208

Abstract

We give a short proof of the following theorem of Sang-hyun Kim: if\nA(\Γ) is a right-angled Artin group with defining graph \Γ, then\nA(\Γ) contains a hyperbolic surface subgroup if \Γ contains an\ninduced subgraph \C_n for some n \≥ 5, where \C_n denotes the\ncomplement graph of an n-cycle. Furthermore, we give a new proof of Kim's\nco-contraction theorem.\n

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• Indecomposable surface bundles over surfaces

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