Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots

2001/08/01 by Lee Rudolph, Rudolph, Lee
Computer Science · Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0108006

16 pages, 13 figures

arxiv created 2001/08/01 · arxiv updated 2009/11/30

Abstract

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.

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