\(K\)-theory of the chair tiling via \(AF\)-algebras (Q295780)

As pointed out in the abstract, but modified, the \(K\)-theory groups for the groupoid \(C^*\)-algebra of the chair tiling are computed by using a new method in the following sense. For computing the \(K\)-theory groups and their generators, the Putnam's six-term exact sequence of \(K\)-theory groups for groupoid \(C^*\)-algebras is used to reduce the computation to those of AF \(C^*\)-algebras associated to the substitution as well as the induced lower dimensional substitutions on edges and vertices of the tiling.NEWLINENEWLINENote that the chair tiling consists of thick \(L\) form blocks, each of which is comprised of three squares joined along edges, directed with angles of rotation, to cover the 2-dimensional plane properly. For the six-term exact sequence of \textit{I. F. Putnam}, see [J. Oper. Theory 38, No. 1, 151--171 (1997; Zbl 0883.46043)].