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

William Norledge, Anne Thomas, Alina Vdovina

Research output: Contribution to journalArticle

Abstract

We give an explicit construction of a maximal torsion-free finite-index subgroup of a certain type of Coxeter group. The subgroup is constructed as the fundamental group of a finite and non-positively curved polygonal complex. First we consider the special case where the universal cover of this polygonal complex is a hyperbolic building, and we construct finite-index embeddings of the fundamental group into certain cocompact lattices of the building. We show that in this special case the fundamental group is an amalgam of surface groups over free groups. We then consider the general case, and construct a finite-index embedding of the fundamental group into the Coxeter group whose Davis complex is the universal cover of the polygonal complex. All of the groups which we embed have minimal index among torsion-free subgroups, and therefore are maximal among torsion-free subgroups.

Original languageEnglish (US)
Pages (from-to)121-143
Number of pages23
JournalGeometriae Dedicata
Volume193
Issue number1
DOIs
StatePublished - Apr 1 2018

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Torsion-free
Fundamental Group
Subgroup
Universal Cover
Coxeter Group
Amalgam
Free Group
Buildings

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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abstract = "We give an explicit construction of a maximal torsion-free finite-index subgroup of a certain type of Coxeter group. The subgroup is constructed as the fundamental group of a finite and non-positively curved polygonal complex. First we consider the special case where the universal cover of this polygonal complex is a hyperbolic building, and we construct finite-index embeddings of the fundamental group into certain cocompact lattices of the building. We show that in this special case the fundamental group is an amalgam of surface groups over free groups. We then consider the general case, and construct a finite-index embedding of the fundamental group into the Coxeter group whose Davis complex is the universal cover of the polygonal complex. All of the groups which we embed have minimal index among torsion-free subgroups, and therefore are maximal among torsion-free subgroups.",
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Maximal torsion-free subgroups of certain lattices of hyperbolic buildings and Davis complexes. / Norledge, William; Thomas, Anne; Vdovina, Alina.

In: Geometriae Dedicata, Vol. 193, No. 1, 01.04.2018, p. 121-143.

Research output: Contribution to journalArticle

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