Maximal torsion-free subgroups of certain lattices of hyperbolic\n buildings and Davis complexes

2016/07/06 by William Norledge, Norledge, William, Anne Thomas +3
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1607.01678

openalex publication_date 2016/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit construction of a maximal torsion-free finite-index\nsubgroup of a certain type of Coxeter group. The subgroup is constructed as the\nfundamental group of a finite and non-positively curved polygonal complex.\nFirst we consider the special case where the universal cover of this polygonal\ncomplex is a hyperbolic building, and we construct finite-index embeddings of\nthe fundamental group into certain cocompact lattices of the building. We show\nthat in this special case the fundamental group is an amalgam of surface groups\nover free groups. We then consider the general case, and construct a\nfinite-index embedding of the fundamental group into the Coxeter group whose\nDavis complex is the universal cover of the polygonal complex. All of the\ngroups which we embed have minimal index among torsion-free subgroups, and\ntherefore are maximal among torsion-free subgroups.\n

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