Aperiodicity, rotational tiling spaces and topological space groups

DOI10.1016/j.aim.2021.107855zbMath1481.37019arXiv1806.00670OpenAlexW2908930099MaRDI QIDQ2042011

James J. Walton, John Robert Hunton

Publication date: 26 July 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.00670

zbMATH Keywords

rotationsgroup cohomologyshape theoryaperiodic tilingscrystallographic groupstiling spacesspace groups

Mathematics Subject Classification ID

Quasicrystals and aperiodic tilings in discrete geometry (52C23) Tiling dynamics (37B52)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the notions of symmetry and aperiodicity for Delone sets
• Tiling spaces, codimension one attractors and shape
• The Ruelle-Sullivan map for actions of \(\mathbb R^n\)
• Spaces of tilings, finite telescopic approximations and gap-labeling
• The geometry of Markoff numbers
• The orientability of matchbox manifolds
• On spaces with the same \(n\)-type for all \(n\)
• The pinwheel tilings of the plane
• Integral cohomology of rational projection method patterns
• Shape of matchbox manifolds
• \(K\)-theory of crossed products of tiling \(C^*\)-algebras by rotation groups
• Mathematics of aperiodic order
• Pattern-equivariant homology
• Homogeneous matchbox manifolds
• Exact regularity and the cohomology of tiling spaces
• Maximal equicontinuous factors and cohomology for tiling spaces
• COHOMOLOGY OF THE PINWHEEL TILING
• Cohomology of substitution tiling spaces
• Topological invariants for projection method patterns
• Complexity and cohomology for cut-and-projection tilings
• The superspace groups for incommensurate crystal structures with a one-dimensional modulation
• Crystallography and Cohomology of Groups
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Topological invariants for substitution tilings and their associated $C^\ast$-algebras
• Pattern-equivariant functions and cohomology
• Applications of group cohomology to the classification of quasicrystal symmetries
• Cohomology of rotational tiling spaces
• The projective fundamental group of a ℤ²-shift
• Manifold-like matchbox manifolds
• Remarks on the cohomology of finite fundamental groups of 3-manifolds
• Pattern-equivariant cohomology with integer coefficients
• Inducing approximations homotopic to maps between inverse limits

This page was built for publication: Aperiodicity, rotational tiling spaces and topological space groups