Aula Magna - Dipartimento di Matematica
The handle number, or Morse-Novikov number, of a knot counts the minimum number of handles needed for a circular Heegaard splitting of its exterior. It may be viewed as a measure of distance from fiberedness. The rank of the top groups of the instanton and Heegaard knot Floer homologies also provide another measure. Here we show that the nearly fibered knots of the Floer sense due to Li-Ye and Baldwin-Sivek are not always nearly fibered in the handle number sense. In the process we also provide conditions for knots to have unique incompressible Seifert surfaces and show that some Floer nearly-fibered knots have incompressible Seifert surfaces of non-minimal genus.