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(Joint work with Lukas Lewark).  Rasmussen's invariant from perturbed Khovanov cohomology is a concordance homomorphism to the integers which also gives a lower bound on the smooth slice genus.  Khovanov-Rozansky sl(n) cohomology generalizes Khovanov cohomology (which appears as the case n=2) and perturbations of it give rise both to a slew of concordance homomorphisms which are also lower bounds as well as to lower bounds which are not equivalent to concordance homomorphisms.  For the case n=2 there is essentially only one perturbation, while already perturbations of the case n=3 exhibit complicated behavior.  We shall discuss this.