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Cocycles on Tiling Spaces

  • Aditya Thorat
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Abstract

The space of tilings by rectangles form an interesting collection of multidimensional subshifts. Here, we study cocycles on such tiling spaces and provide an algorithmically decidable necessary and sufficient condition for the tiling space associated with a collection of rectangles to admit a nontrivial cocycle. Along the way, we also prove that the tiling spaces corresponding to a class of rectangular tile sets satisfy certain mixing properties.

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Cite

BibTeXRIS
BibTeX
@misc{thorat2026cocycles,
  title = {{Cocycles on Tiling Spaces}},
  author = {Aditya Thorat},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39907},
  eprint = {2610.39907},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39907},
}
RIS
TY  - UNPB
TI  - Cocycles on Tiling Spaces
AU  - Aditya Thorat
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39907
UR  - https://arxiv.org/abs/2610.39907
AB  - The space of tilings by rectangles form an interesting collection of multidimensional subshifts. Here, we study cocycles on such tiling spaces and provide an algorithmically decidable necessary and sufficient condition for the tiling space associated with a collection of rectangles to admit a nontrivial cocycle. Along the way, we also prove that the tiling spaces corresponding to a class of rectangular tile sets satisfy certain mixing properties.
ER  -