Work

Supersolvable posets and fiber-type abelian arrangements

Year: 2024

Type: article

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 $$K(\pi ,1)$$ 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.

Source: Selecta Mathematica

DOI: 10.1007/s00029-024-00976-w

Authors: Christin Bibby, Emanuele Delucchi

Institutions: Louisiana State University, University of Applied Sciences and Arts of Southern Switzerland, Dalle Molle Institute for Artificial Intelligence Research

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Mathematisches Forschungsinstitut Oberwolfach