The K ( π , 1 ) conjecture for Artin groups of spherical type

In these notes, we introduce the 50-year-old K ( π , 1 ) conjecture alongside Coxeter and Artin groups. Roughly speaking, the conjecture states that the complement in ℂ n of a “symmetric” configuration of hyperplanes is a K ( π , 1 ) space. Our end goal is to present a proof of the conjecture in the so-called spherical case, where only a finite number of hyperplanes are removed, through methods from combinatorial topology. This proof draws inspiration from the original proof of the spherical case, which is a special case of a celebrated 1972 theorem by Pierre Deligne.