Density of commensurators for uniform lattices of right-angled buildings

Surface Quotients of Hyperbolic Buildings

“…We finally note that since all local groups of G(Y ) are direct products of cyclic groups, it seems possible that all of its nontrivial local groups (not just the nontrivial face groups) could be killed using a construction similar to that in [1] or [15], so as to obtain the infinite polygonal complex Y g = π 1 (S g )\I p,v explicitly.…”

“…In this topology, a uniform lattice in G is a subgroup Γ < G acting cocompactly on I p,v with finite cell stabilizers (see Section 2.2 below). Bourdon's building and its lattices have been studied by, for example, Bourdon [4], Bourdon-Pajot [5], Haglund [9,10,11], Kubena-Thomas [15], Ledrappier-Lim [16], Rémy [18], Thomas [20], and Vdovina [21].…”

“…The Γ p,v,g so obtained are a new family of uniform lattices. In particular, they are not graph products of finite groups, as considered in [4,11], nor are they constructed from such graph products as in [15], nor are they fundamental groups of finite polyhedra as in [21], nor do they "come from" tree lattices as do the lattices in [20].…”