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Mathematics > Combinatorics
Title: Supersolvable posets and fiber-type abelian arrangements
(Submitted on 24 Feb 2022 (v1), last revised 25 Apr 2024 (this version, v2))
Abstract: 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($\pi$,1) toric and elliptic arrangements. Under a stronger combinatorial condition, we prove a factorization of the Poincar\'e polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk-Randell's formula relating the Poincar\'e polynomial to the lower central series of the fundamental group.
Submission history
From: Christin Bibby [view email][v1] Thu, 24 Feb 2022 10:12:01 GMT (36kb)
[v2] Thu, 25 Apr 2024 23:52:58 GMT (38kb)
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