 

Jason S. Kimberley and Guyan Robertson
Groups acting on products of trees, tiling systems and analytic Ktheory


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


Abstract
Let T_{1} and T_{2} be homogeneous trees of even degree ≧ 4. A BM group Γ is a torsionfree discrete subgroup of Aut(T_{1})×Aut(T_{2})
which acts freely and transitively on the vertex set of T_{1}×T_{2}.
This article studies dynamical systems associated with BM groups.
A higher rank CuntzKrieger algebra A(Γ) is associated both with a 2dimensional tiling system and with a boundary action of a BM group Γ. An explicit expression is given for the Ktheory of A(Γ). In particular K_{0}=K_{1}.
A complete enumeration of possible BM groups Γ is given for a product homogeneous trees of degree 4, and the Kgroups are computed.


Acknowledgements
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
guyan@maths.newcastle.edu.au
http://www.maths.newcastle.edu.au/~guyan/
jascki@iprimus.com.au

