Finite group extensions and the Baum–Connes conjecture

Abstract

In this note, we exhibit a method to prove the Baum–Connes conjecture (with coefficients) 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 $S^3$.