Supersolvable posets and fiber-type abelian arrangements
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913329339957248 |
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| author | Bibby, Christin Delucchi, Emanuele |
| author_facet | Bibby, Christin Delucchi, Emanuele |
| contents | We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell-Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. This is consistent with Terao's fibration theorem connecting bundles of hyperplane arrangements to Stanley's lattice supersolvability. We obtain a combinatorially determined class of K($π$,1) toric and elliptic arrangements. Under a stronger combinatorial condition, we prove a factorization of the Poincaré polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk-Randell's formula relating the Poincaré polynomial to the lower central series of the fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11996 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Supersolvable posets and fiber-type abelian arrangements Bibby, Christin Delucchi, Emanuele Combinatorics Algebraic Topology 06A07, 55R80 We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell-Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. This is consistent with Terao's fibration theorem connecting bundles of hyperplane arrangements to Stanley's lattice supersolvability. We obtain a combinatorially determined class of K($π$,1) toric and elliptic arrangements. Under a stronger combinatorial condition, we prove a factorization of the Poincaré polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk-Randell's formula relating the Poincaré polynomial to the lower central series of the fundamental group. |
| title | Supersolvable posets and fiber-type abelian arrangements |
| topic | Combinatorics Algebraic Topology 06A07, 55R80 |
| url | https://arxiv.org/abs/2202.11996 |