Infinite Translation Surfaces in the Wild
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914708185939968 |
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| author | Delecroix, Vincent Hubert, Pascal Valdez, Ferrán |
| author_facet | Delecroix, Vincent Hubert, Pascal Valdez, Ferrán |
| contents | This book explores infinite-type translation surfaces and is intended as an introductory text for graduate and PhD students, as well as a reference for more advanced researchers.
Chapter 1 introduces the three definitions of translation surfaces and meticulously proves their equivalence. It is enriched with numerous examples that are revisited throughout the book.
Chapter 2 provides a detailed examination of the topological classification of infinite-type surfaces, the construction of infinite coverings of finite-type translation surfaces, and the structure of points within the metric completion.
Chapter 3 investigates the affine symmetries of infinite-type translation surfaces, with special emphasis on infinite coverings of finite-type surfaces, the Hooper-Thurston-Veech construction, and affine homeomorphisms of finite-area infinite-type translation surfaces.
Chapter 4 introduces infinite interval exchange transformations and employs them to demonstrate that the dynamics of translation flows are significantly more complex in the infinite-type context.
The two appendices address hyperbolic geometry and the spectra of infinite graphs, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite Translation Surfaces in the Wild Delecroix, Vincent Hubert, Pascal Valdez, Ferrán Geometric Topology Dynamical Systems 37E30, 30F30, 37E35, 37A40 This book explores infinite-type translation surfaces and is intended as an introductory text for graduate and PhD students, as well as a reference for more advanced researchers. Chapter 1 introduces the three definitions of translation surfaces and meticulously proves their equivalence. It is enriched with numerous examples that are revisited throughout the book. Chapter 2 provides a detailed examination of the topological classification of infinite-type surfaces, the construction of infinite coverings of finite-type translation surfaces, and the structure of points within the metric completion. Chapter 3 investigates the affine symmetries of infinite-type translation surfaces, with special emphasis on infinite coverings of finite-type surfaces, the Hooper-Thurston-Veech construction, and affine homeomorphisms of finite-area infinite-type translation surfaces. Chapter 4 introduces infinite interval exchange transformations and employs them to demonstrate that the dynamics of translation flows are significantly more complex in the infinite-type context. The two appendices address hyperbolic geometry and the spectra of infinite graphs, respectively. |
| title | Infinite Translation Surfaces in the Wild |
| topic | Geometric Topology Dynamical Systems 37E30, 30F30, 37E35, 37A40 |
| url | https://arxiv.org/abs/2403.05424 |