How big is a tiling's return module?
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917690710425600 |
|---|---|
| author | Perryman, Abigail Sadun, Lorenzo |
| author_facet | Perryman, Abigail Sadun, Lorenzo |
| contents | The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology $\check H^1(Ω)$ gives upper and lower bounds for the size of the return module. For all sufficiently large patches, the rank of the return module is at most the same as the rank of the cohomology. For a generic choice of tile shapes and an arbitrary reference patch, the rank of the return module is at least the rank of $\check H^1(Ω)$. Therefore, for generic tile shapes and sufficiently large patches, the rank of the return module is equal to the rank of $\check H^1(Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How big is a tiling's return module? Perryman, Abigail Sadun, Lorenzo Dynamical Systems 37B52, also 37C79, 52C22, 52C23, 55N05 The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology $\check H^1(Ω)$ gives upper and lower bounds for the size of the return module. For all sufficiently large patches, the rank of the return module is at most the same as the rank of the cohomology. For a generic choice of tile shapes and an arbitrary reference patch, the rank of the return module is at least the rank of $\check H^1(Ω)$. Therefore, for generic tile shapes and sufficiently large patches, the rank of the return module is equal to the rank of $\check H^1(Ω)$. |
| title | How big is a tiling's return module? |
| topic | Dynamical Systems 37B52, also 37C79, 52C22, 52C23, 55N05 |
| url | https://arxiv.org/abs/2406.07501 |