|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Dual structures on
Coxeter and Artin groups of rank three
Emanuele Delucchi, Giovanni Paolini and Mario Salvetti |
|
Geometry & Topology 28 (2024) 4295–4336
|
 |
Abstract |
|
We extend the theory of dual Coxeter and Artin groups to all rank-three Coxeter systems, beyond the previously studied spherical and affine cases. Using geometric, combinatorial, and topological techniques, we show that rank-three noncrossing partition posets are EL–shellable lattices and give rise to Garside groups isomorphic to the associated standard Artin groups. Within this framework, we prove the conjecture, the triviality of the center, and the solubility of the word problem for rank-three Artin groups. Some of our constructions apply to general Artin groups; we hope they will help develop complete solutions to the conjecture and other open problems in the area. |
Keywords
Artin groups, Coxeter groups, Garside structures, discrete
Morse theory, shellability
|
Mathematical Subject Classification
Primary: 20F36, 20F55
Secondary: 06A07, 55P20, 55R35, 57Q70
|
References |
Publication
Received: 13 July 2022
Revised: 15 May 2023
Accepted: 15 June 2023
Published: 27 December 2024
Proposed: Mladen Bestvina
Seconded: Ian Agol, Martin R Bridson
|
Authors |
| Emanuele Delucchi | |
| IDSIA University of Applied Arts and Sciences of Southern Switzerland Lugano Switzerland |
|
| Giovanni Paolini | |
| Dipartimento di Matematica Università di Bologna Bologna Italy |
|
| Mario Salvetti | |
| Dipartimento di Matematica Università di Pisa Pisa Italy |
|
| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
