L-spaces, taut foliations and fibred hyperbolictwo-bridge links

We prove that if M is a rational homology sphere that is Dehn surgery on a fibred hyperbolic two-bridge link, then M is not an L-space if and only if M supports a co-orientable taut foliation.As a corollary we show that if K 0 is obtained by a nontrivial knot K as a result of an operation called two-bridge replacement, then all nonmeridional surgeries on K 0 support co-orientable taut foliations.This operation generalises Whitehead doubling and as a particular case we deduce that all nonmeridional surgeries on Whitehead doubles of a nontrivial knot support co-orientable taut foliations.