%0 Journal Article
%T Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots
%A Lee Rudolph
%J Mathematics
%D 2001
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0108006v1