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Session S28 - Knots, Surfaces, 3-manifolds

Wednesday, July 14, 18:00 ~ 18:30 UTC-3

On classification of genus $g$ knots which admit a $(1,1)$-decomposition

Fabiola Manjarrez-Gutiérrez

UNAM, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Given an oriented minimal genus Seifert surface $F'$ for a $(1,1)$-knot $K$ it is possible to surger $F'$ along annuli to obtain a simple minimal Seifert surface $F$. Such a surface can be put in a very nice position with respect to the $(1,1)$-position of the knot $K$. Using this kind of surfaces we give a description of a $(1,1)$-knot of genus $g$ as a vertical banding of $(1,1)$-knots of genus smaller than $g$. In addition, we show that any rational knot of genus $g$ is obtained as a vertical banding of $g$ genus one rational knots.

Joint work with Mario Eudave-Muñoz (UNAM) and Enrique Ramírez-Losada (CIMAT).

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