On the $K$-theory of $C^*$-algebras associated to substitution tilings

DOI10.4064/dm800-4-2020zbMath1472.46073arXiv1712.09551OpenAlexW3048289739MaRDI QIDQ5856644

Maria Ramirez-Solano, Daniel Gonçalves

Publication date: 29 March 2021

Published in: Dissertationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09551

zbMATH Keywords

substitution tilings$K$-theory

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Morse-Smale systems (37D15)

Related Items (1)

Shadowing, finite order shifts and ultrametric spaces

Cites Work

• \(K\)-theory of the chair tiling via \(AF\)-algebras
• On the K-theory of the stable C\(^{*}\)-algebras from substitution tilings
• The Ruelle-Sullivan map for actions of \(\mathbb R^n\)
• Spaces of tilings, finite telescopic approximations and gap-labeling
• A groupoid approach to C*-algebras
• Finite rank torsion free Abelian groups and rings
• The Novikov conjecture for hyperbolic foliations
• The structure of \(C^*\)-algebras associated with hyperbolic dynamical systems
• The Baum-Connes conjecture for amenable foliations
• The local structure of tilings and their integer group of coinvariants
• Induced representations of C\(^*\)-algebras
• Cohomology of one-dimensional mixed substitution tiling spaces
• Pattern-equivariant homology
• K-theoretic duality for hyperbolic dynamical systems
• Exact regularity and the cohomology of tiling spaces
• A non-amenable groupoid whose maximal and reduced $C^*$-algebras are the same
• Cohomology of substitution tiling spaces
• When shape matters: deformations of tiling spaces
• Cohomology in one-dimensional substitution tiling spaces
• Topological invariants for substitution tilings and their associated $C^\ast$-algebras
• Pattern-equivariant functions and cohomology
• Continuous-trace groupoid 𝐶*-algebras. III
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• C*-Algebras from Smale Spaces
• Pattern-equivariant cohomology with integer coefficients
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