Tiling systems and homology of lattices in tree products

Abstract: Let

G a m m a

be a torsion free cocompact lattice in

a u t (c l T_{1}) i m e s a u t (c l T_{2})

, where

c l T_{1}

,

c l T_{2}

are trees whose vertices all have degree at least three. The group

is determined explicitly in terms of an associated 2-dimensional tiling system. It follows that under appropriate conditions the crossed product

C^{*}

-algebra

c l A

associated with the action of

G a m m a

on the boundary of

c l T_{1} i m e s c l T_{2}

satisfies

.

Full work available at URL: https://arxiv.org/abs/math/0511447

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