26 citations · 59 across the 12 of their papers we have counts for
6 papers · 1 filter
K-theory of the Chair Tiling via AF-algebras
Antoine Julien, Jean Savinien
We compute the -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 -the…
On the noncommutative geometry of tilings
Antoine Julien, Johannes Kellendonk, Jean Savinien
This is a chapter in an incoming book on aperiodic order. We review results about the topology, the dynamics, and the combinatorics of aperiodically ordered tilings obtained with t…
Spectral triples from stationary Bratteli diagrams
Johannes Kellendonk, Jean Savinien
We construct spectral triples for path spaces of stationary Bratteli diagrams and study their associated mathematical objects, in particular their zeta function, their heat kernel…
Spectral triples and aperiodic order
J. Kellendonk, J. Savinien
We construct spectral triples for compact metric spaces (X, d). This provides us with a new metric d_s on X. We study its relation with the original metric d. When X is a subshift…
Tiling groupoids and Bratteli diagrams
J. Bellissard, A. Julien, J. Savinien
Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the…
Transverse Laplacians for Substitution Tilings
Antoine Julien, Jean Savinien
Pearson and Bellissard recently built a spectral triple - the data of Riemanian noncommutative geometry - for ultrametric Cantor sets. They derived a family of Laplace-Beltrami lik…