  Murasugi sums can be defined as readily for Morse maps to the circle of
(arbitrary) link complements in the 3-sphere as for fibrations over the circle
of (fibered) link complements in the 3-sphere. As one application, I show that
if a knot K has free genus m, then there is a Morse map from its complement to
the circle (representing the relative homology class of a Seifert surface for
K) with no more than 4m critical points.
