# Proof of the $K(\pi,1)$ conjecture for affine Artin groups

@inproceedings{Paolini2019ProofOT, title={Proof of the \$K(\pi,1)\$ conjecture for affine Artin groups}, author={Giovanni Paolini and Mario Salvetti}, year={2019} }

We prove the $K(\pi,1)$ 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… CONTINUE READING

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