Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K
is sufficiently complicated, then Dehn surgery on K cannot yield a lens space.
Work of Yi Ni shows that if K has a lens space surgery then it is fibered.
Combining this with our result we see that if K has a lens space surgery then
it is fibered and the monodromy is relatively simple
