A Homeomorphism Invariant for Substitution Tiling Spaces
Dynamical Systems
2018-07-11 v1 Algebraic Topology
K-Theory and Homology
Abstract
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Cech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value.
Cite
@article{arxiv.math/0008171,
title = {A Homeomorphism Invariant for Substitution Tiling Spaces},
author = {Nic Ormes and Charles Radin and Lorenzo Sadun},
journal= {arXiv preprint arXiv:math/0008171},
year = {2018}
}
Comments
32 pages, including 9 embedded figures