K-theory of the Chair Tiling via AF-algebras

Abstract

We compute the K-theory groups of the groupoid C * -algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the K-theory groups of the AF -algebras of the substitution and the induced lower dimensional substitutions on edges and vertices.Key words and phrases. aperiodic tiling; K-theory; C * -algebra; groupoid. 1 Often, it is technically simpler to study a Morita-equivalent C * -algebra corresponding to the reduction of Ω R d on a transversal.