New York Journal of Mathematics
Volume 8 (2002) 111-131


Jason S. Kimberley and Guyan Robertson

Groups acting on products of trees, tiling systems and analytic K-theory

Published: August 9, 2002
Keywords: group actions, trees, K-theory, C*-algebras.
Subject: Primary 20E08, 51E24; secondary 46L80

Let T1 and T2 be homogeneous trees of even degree ≧ 4. A BM group Γ is a torsion-free discrete subgroup of Aut(T1)×Aut(T2) which acts freely and transitively on the vertex set of T1×T2. This article studies dynamical systems associated with BM groups. A higher rank Cuntz-Krieger algebra A(Γ) is associated both with a 2-dimensional tiling system and with a boundary action of a BM group Γ. An explicit expression is given for the K-theory of A(Γ). In particular K0=K1. A complete enumeration of possible BM groups Γ is given for a product homogeneous trees of degree 4, and the K-groups are computed.


This research was funded by the Australian Research Council. The second author is also grateful for the support of the University of Geneva.

Author information

Mathematics Department, University of Newcastle, Callaghan, NSW 2308, Australia