5 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…
Circular handle decompositions of free genus one knots
Fabiola Manjarrez-Gutiérrez, Víctor Núñez, Enrique Ramírez-Losada
We determine the structure of the circular handle decompositions of the family of free genus one knots. Namely, if k is a free genus one knot, then the handle number h(k)= 0, 1 or…