The K(, 1) Conjecture for the Affine Braid Groups
by
Ruth Charney
Ohio State University
Coauthors: David Peifer

If W is a finite Coxeter group acting as a reflection group, one can complexify the action and remove the (complex) hyperplanes fixed by reflections in W. Then W acts freely on the resulting space X, and the quotient X/W is a K(\pi, 1)-space for the associated Artin group. An analogous statement is conjectured to hold for infinite Coxeter groups. We prove that this conjecture holds for the Euclidean Coxeter groups of type tilde A_n, whose associated Artin groups are known as the affine braid groups. The proof involves a constructing a new K(\pi, 1)-space for these groups.

Date received: March 1, 2002