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2 results for “EL-shellability”

Proof of the

K(π,1)

conjecture for affine Artin groupsmath.GR

We prove a long-standing conjecture about complex reflection arrangements.

problem The

K(π,1)

conjecture for affine Artin groups.

method Recent advancements in dual Coxeter and Artin groups theory, new constructions, and poset shellability.

result The complexified complement of an affine reflection arrangement is a classifying space.

Artin groups reflection arrangements classifying spaces Coxeter groups EL-shellability

2019-07-26abs ↗pdf ↗

Dual structures on Coxeter and Artin groups of rank threemath.GR

Extended dual Coxeter and Artin groups theory to rank-three systems.

problem Extend dual Coxeter and Artin groups theory to rank-three systems.

method Geometric, combinatorial, and topological techniques.

result Proved the

K(π, 1)

conjecture, triviality of the center, and solubility of the word problem for rank-three Artin groups.

Coxeter groups Artin groups rank-three dual groups K(π

2022-06-29abs ↗pdf ↗