Dual approach to the $K(\pi, 1)$−conjecture for Artin groups

Mario Salvetti, University of Pisa

Online Talk

We examine the $K(\pi, 1)$-conjecture for Artin groups, a problem dating back to the 1970’s

and originally attributed to Arnol’d, Thom, Brieskorn, and Pham. It was proven by Deligne ([Inv. Math., ’72])

in the spherical case and recently ([G. Paolini, M. Sal., Inv. Math., ’21]) in the affine case. We provide an

overview of the methods employed, primarily focusing on the so-called ’dual approach,’ and we mention

some more recent results about further cases where these methods work.