Monodromy of supersolvable toric arrangements
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917480192016384 |
|---|---|
| author | Bibby, Christin Cohen, Daniel C. Delucchi, Emanuele |
| author_facet | Bibby, Christin Cohen, Daniel C. Delucchi, Emanuele |
| contents | We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces. In the toric case, we show that the monodromy of a supersolvable arrangement bundle factors through the Artin braid group, and that of a strictly supersolvable arrangement bundle factors further through the Artin pure braid group. The latter factorization is particularly informative -- we use it to determine a number of invariants of the complement of a strictly supersolvable arrangement, including the cohomology ring and the lower central series Lie algebra of the fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monodromy of supersolvable toric arrangements Bibby, Christin Cohen, Daniel C. Delucchi, Emanuele Algebraic Topology Combinatorics 55R10, 55R80 We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces. In the toric case, we show that the monodromy of a supersolvable arrangement bundle factors through the Artin braid group, and that of a strictly supersolvable arrangement bundle factors further through the Artin pure braid group. The latter factorization is particularly informative -- we use it to determine a number of invariants of the complement of a strictly supersolvable arrangement, including the cohomology ring and the lower central series Lie algebra of the fundamental group. |
| title | Monodromy of supersolvable toric arrangements |
| topic | Algebraic Topology Combinatorics 55R10, 55R80 |
| url | https://arxiv.org/abs/2510.00166 |