Exact regularity and the cohomology of tiling spaces

DOI10.1017/S0143385710000611zbMath1271.37018arXiv1004.2281OpenAlexW2964262298MaRDI QIDQ2884099

Lorenzo Sadun

Publication date: 24 May 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2281

zbMATH Keywords

cohomologytiling spacesexact regularityhomological Pisot substitutions

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (11)

Balancedness and coboundaries in symbolic systems ⋮ Integral cohomology of rational projection method patterns ⋮ Self affine Delone sets and deviation phenomena ⋮ Random substitution tilings and deviation phenomena ⋮ Aperiodicity, rotational tiling spaces and topological space groups ⋮ Rotation numbers and rotation classes on one-dimensional tiling spaces ⋮ Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\) ⋮ Substitutions with vanishing rotationally invariant first cohomology ⋮ Statistics of patterns in typical cut and project sets ⋮ On the $K$-theory of $C^*$-algebras associated to substitution tilings ⋮ Tilings and traces

Cites Work

• The Ruelle-Sullivan map for actions of \(\mathbb R^n\)
• Spaces of tilings, finite telescopic approximations and gap-labeling
• The pinwheel tilings of the plane
• 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
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• Pattern-equivariant cohomology with integer coefficients

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