Topological equivalence of tilings
arXiv:cond-mat/9609254 · doi:10.1063/1.531915
Abstract
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are topologically equivalent whenever their associated groupoids are isomorphic.
23 pages, Latex2e, uses amsart-style, no figures
References in corpus (1)
Cited by in corpus (23)
- Operator theory of electrical resistance networks
- A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
- A perspective on non-commutative frame theory
- General Non-Commutative Locally Compact Locally Hausdorff Stone Duality
- Pinwheel patterns and powder diffraction
- Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
- A Homeomorphism Invariant for Substitution Tiling Spaces
- K-theory for semigroup C*-algebras and partial crossed products
- Rigidity properties of full groups of pseudogroups over the Cantor set
- Distributive inverse semigroups and non-commutative Stone dualities
- C*-algebras of Boolean inverse monoids - traces and invariant means
- The tiling C*-algebra viewed as a tight inverse semigroup algebra
- Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras
- On a class of countable Boolean inverse monoids and Matui's spatial realization theorem
- A non-commutative generalization of Stone duality
- On an order based construction of a groupoid from an inverse semigroup
- Pseudogroups and their etale groupoids
- Universal groups for point-sets and tilings
- Tiling spaces are covering spaces over irrational tori
- Topological invariants for projection method patterns
- Two partial monoid structures on a set
- The etale groupoid of an inverse semigroup as a groupoid of filters
- Pattern equivariant functions, deformations and equivalence of tiling spaces