  It is well-known that generic perturbations of the complex Frobenius algebra
used to define Khovanov cohomology each give rise to Rasmussen's concordance
invariant s. This gives a concordance homomorphism to the integers and a strong
lower bound on the smooth slice genus of a knot. Similar behavior has been
observed in sl(n) Khovanov-Rozansky cohomology, where a perturbation gives rise
to the concordance homomorphisms s_n for each n >= 2, and where we have s_2 =
s. We demonstrate that s_n for n >= 3 does not in fact arise generically, and
that varying the chosen perturbation gives rise both to new concordance
homomorphisms as well as to new sliceness obstructions that are not equivalent
to concordance homomorphisms.
