4 papers
Handle number is not always realized by a minimal genus Seifert surface
Kenneth L. Baker, Fabiola Manjarrez-Gutiérrez
We construct genus one knots whose handle number is only realized by Seifert surfaces of non-minimal genus. These are counterexamples to the conjecture that the Seifert genus of a…
Handle numbers of guts of sutured manifolds and nearly fibered knots
Kenneth L. Baker, Fabiola Manjarrez-Gutiérrez
Extending Haken's Theorem to product annuli and disks for Heegaard splittings of sutured manifolds, we show that the handle number of an irreducible sutured manifold equals the han…
Morse-Novikov numbers, tunnel numbers, and handle numbers of sutured manifolds
Kenneth L. Baker, Fabiola Manjarrez-Gutiérrez
Developed from geometric arguments for bounding the Morse-Novikov number of a link in terms of its tunnel number, we obtain upper and lower bounds on the handle number of a Heegaar…
Computing Genera of Satellite Tunnel Number One Knots and Torti-rational Knots
Mario Eudave-Muñoz, Fabiola Manjarrez-Gutiérrez, Enrique Ramírez-Losada +1
The genus of satellite tunnel number one knots and torti-rational knots is computed using the tools introduced by Floyd and Hatcher. An implementation of an algorithm is given to c…