New York Journal of Mathematics
Volume 11 (2005) 635-647


Guyan Robertson

Tiling systems and homology of lattices in tree products

Published: December 14, 2005
Keywords: tree products, lattices, homology, K-theory, operator algebra
Subject: 22E40, 22D25

Let Γ be a torsion-free cocompact lattice in Aut(T1) × Aut(T2), where T1, T2 are trees whose vertices all have degree at least three. The group H2(Γ, Z) is determined explicitly in terms of an associated 2-dimensional tiling system. It follows that under appropriate conditions the crossed product C*-algebra A associated with the action of Γ on the boundary of T1×T2 satisfies rank K0(A) = 2⋅rank H2(Γ, Z).

Author information

School of Mathematics and Statistics, University of Newcastle, NE1 7RU, U.K.