Artin K(pi,1) Conjecture

The Artin conjecture asserts that the Artin Salvetti complex of every Artin group with finitely many standard generators is an aspherical space. Equivalently, the universal cover of this CW-complex is contractible, or its homotopy groups satisfy

for every . The higher-dimensional cells are part of the asserted model, not just the cells giving the group presentation.