Finite group extensions and the Baum–Connes conjecture

Abstract

In this note, we exhibit a method to prove the Baum–Connes conjecture (with coef-ficients) for extensions with finite quotients of certain groups which already satisfy the Baum–Connes conjecture. Interesting examples to which this method applies are torsion-free finite extensions of the pure braid groups, eg the full braid groups, and fundamental groups of certain link complements in S 3 .