Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics: "Noncrossing partitions and dual cell structures on hyperplane complement"
Presenter
March 11, 2024
Keywords:
- Artin groups
- braid groups
- Coxeter groups
- reflection groups
- Garside structures
- classifying spaces
- hyperplane arrangements
- subspace arrangements
- configuration spaces
- geometric group theory
- Matroids
- cohomology
MSC:
- 14N20 - Configurations and arrangements of linear subspaces
- 20F36 - Braid groups
- Artin groups
Abstract
Braid groups are the original Artin groups and they have many different classifyng spaces: (1) Quotient of a complex hyperplane complement, (2) Monic polynomials with distinct roots, (3) Salvetti complex from face-identifying a permutahedron, and (4) Dual braid complex from face-identifying the order complex of the noncrossing partition lattice. This talk connects the hyperplane complement and the monic polynomials to the noncrossing partitions in the dual structure. It is based on joint work with Michael Dougherty.