An illustrated introduction to the coarse topology of lamplighters
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916964508631040 |
|---|---|
| author | Genevois, Anthony |
| author_facet | Genevois, Anthony |
| contents | Roughly speaking, lamplighter graphs encode the possible configurations of a lamplighter that moves along a given graph and that modifies the colours of lamps at vertices. This article is dedicated to the following delicate question: when do two lamplighter graphs have the same coarse geometry, i.e.\ when are they quasi-isometric? Inspired by elementary ideas from topology, which we will ``coarsify'', I will survey some techniques that allow us to compare efficiently lamplighter graphs (and more) up to quasi-isometry. Based on a minicourse given during the Journées de Topologie Géométrique at the Institut Fourier in August 2025. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An illustrated introduction to the coarse topology of lamplighters Genevois, Anthony Group Theory Geometric Topology Metric Geometry 20F65, 20F69 Roughly speaking, lamplighter graphs encode the possible configurations of a lamplighter that moves along a given graph and that modifies the colours of lamps at vertices. This article is dedicated to the following delicate question: when do two lamplighter graphs have the same coarse geometry, i.e.\ when are they quasi-isometric? Inspired by elementary ideas from topology, which we will ``coarsify'', I will survey some techniques that allow us to compare efficiently lamplighter graphs (and more) up to quasi-isometry. Based on a minicourse given during the Journées de Topologie Géométrique at the Institut Fourier in August 2025. |
| title | An illustrated introduction to the coarse topology of lamplighters |
| topic | Group Theory Geometric Topology Metric Geometry 20F65, 20F69 |
| url | https://arxiv.org/abs/2509.18941 |