Proof of the K(π, 1) conjecture for affine Artin groups
| Autor: | Giovanni Paolini, Mario Salvetti |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Classifying space
Pure mathematics General Mathematics 01 natural sciences Mathematics - Geometric Topology Mathematics::Group Theory 0103 physical sciences Mathematics - Combinatorics Mathematics - Algebraic Topology 0101 mathematics Complement (set theory) Mathematics Conjecture Mathematics::Combinatorics Noncrossing partition 010102 general mathematics Coxeter group 20F36 20F55 55P20 Classifyng spaces Artin groups Artin groups Reflection (mathematics) Classifyng spaces 010307 mathematical physics Affine transformation Orbit (control theory) Mathematics - Group Theory |
| Popis: | We prove the $$K(\pi ,1)$$ K ( π , 1 ) conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol’d, Pham, and Thom. Our proof is based on recent advancements in the theory of dual Coxeter and Artin groups, as well as on several new results and constructions. In particular: we show that all affine noncrossing partition posets are EL-shellable; we use these posets to construct finite classifying spaces for dual affine Artin groups; we introduce new CW models for the orbit configuration spaces associated with arbitrary Coxeter groups; we construct finite classifying spaces for the braided crystallographic groups introduced by McCammond and Sulway. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|