On connected subgraph arrangements
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916021439299584 |
|---|---|
| author | Giordani, Lorenzo Möller, Tilman Mücksch, Paul Roehrle, Gerhard |
| author_facet | Giordani, Lorenzo Möller, Tilman Mücksch, Paul Roehrle, Gerhard |
| contents | Recently, Cuntz and Kühne introduced a particular class of hyperplane arrangements stemming from a given graph $G$, so called connected subgraph arrangements $A_G$. In this note we strengthen some of the result from their work and prove new ones for members of this class. For instance, we show that aspherical members withing this class stem from a rather restricted set of graphs. Specifically, if $A_G$ is an aspherical connected subgraph arrangement, then $A_G$ is free with the unique possible exception when the underlying graph $G$ is the complete graph on $4$ nodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On connected subgraph arrangements Giordani, Lorenzo Möller, Tilman Mücksch, Paul Roehrle, Gerhard Combinatorics Algebraic Topology 52C35, 14N20, 20F55, 32S22 Recently, Cuntz and Kühne introduced a particular class of hyperplane arrangements stemming from a given graph $G$, so called connected subgraph arrangements $A_G$. In this note we strengthen some of the result from their work and prove new ones for members of this class. For instance, we show that aspherical members withing this class stem from a rather restricted set of graphs. Specifically, if $A_G$ is an aspherical connected subgraph arrangement, then $A_G$ is free with the unique possible exception when the underlying graph $G$ is the complete graph on $4$ nodes. |
| title | On connected subgraph arrangements |
| topic | Combinatorics Algebraic Topology 52C35, 14N20, 20F55, 32S22 |
| url | https://arxiv.org/abs/2502.18144 |