From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913867737595904 |
|---|---|
| author | Piedade, Claudio Alexandre Tranchida, Philippe |
| author_facet | Piedade, Claudio Alexandre Tranchida, Philippe |
| contents | Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry.
In this article, we build upon that idea by extending classical group-theoretic constructions (amalgamated products, HNN-extensions, semi-direct products, and twisting) to the setting of coset geometries. This gives a general way to glue together incidence geometries in various ways. This provides a general framework for combining or gluing incidence geometries in different ways while preserving essential properties such as flag-transitivity and residual connectedness.
Using these techniques, we analyze families of Shephard groups, which generalize both Coxeter and Artin-Tits groups, and their associated simplicial complexes.
Our results also point to the existence of a Bass-Serre theory for coset geometries and of a fundamental geometry of a graph of coset geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries Piedade, Claudio Alexandre Tranchida, Philippe Group Theory Combinatorics Geometric Topology 20E06, 51E30, 20F55, 20F36 Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon that idea by extending classical group-theoretic constructions (amalgamated products, HNN-extensions, semi-direct products, and twisting) to the setting of coset geometries. This gives a general way to glue together incidence geometries in various ways. This provides a general framework for combining or gluing incidence geometries in different ways while preserving essential properties such as flag-transitivity and residual connectedness. Using these techniques, we analyze families of Shephard groups, which generalize both Coxeter and Artin-Tits groups, and their associated simplicial complexes. Our results also point to the existence of a Bass-Serre theory for coset geometries and of a fundamental geometry of a graph of coset geometries. |
| title | From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries |
| topic | Group Theory Combinatorics Geometric Topology 20E06, 51E30, 20F55, 20F36 |
| url | https://arxiv.org/abs/2505.24662 |