PreprintMaximal torsionfree subgroups of certain lattices of hyperbolic buildings and Davis complexesWilliam Norledge, Anne Thomas and Alina VdovinaAbstractWe give an explicit construction of a maximal torsionfree finiteindex subgroup of a certain type of Coxeter group. The subgroup is constructed as the fundamental group of a finite and nonpositively curved polygonal complex. First we consider the special case where the universal cover of this polygonal complex is a hyperbolic building, and we construct finiteindex 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 finiteindex 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 torsionfree subgroups, and therefore are maximal among torsionfree subgroups. This paper is available as a pdf (508kB) file.
