Georgia Institute of Technology College of Sciences

In the Instanton and Heegaard Floer theories, a nearly fibered knot is one for which the top grading has rank 2. Sivek-Baldwin and Li-Ye showed that the guts (ie. the reduced sutured manifold complement) of a minimal genus Seifert surface of a nearly fibered knot has of one of three simple types.We show that nearly fibered knots with guts of two of these types have handle number 2 while those with guts of the third type have handle number 4.  Furthermore, we show that nearly fibered knots have unique incompressible Seifert surfaces rather than just unique minimal genus Siefert surfaces. This is joint work in progress with Fabiola Manjarrez-Gutierrez.