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Satellite L-space knots are braided satellites*

Banff International Research Station for Mathematical Innovation and Discovery

Let $\{K_n\}$ be the family of knots obtained by twisting a knot K along an unknot c. When the winding number of K about c is non-zero, we show the limit of $g(K_n)/g_4(K_n)$ is 1 if and only if the winding and wrapping numbers of K about c are equal. When equal, this leads to a description of minimal genus Seifert surfaces of $K_n$ for $|n|\gg0$ and eventually to a characterization of when c is a braid axis for K. We then use this characterization to show that satellite L-space knots are braided satellites*. This is joint work with Kimihiko Motegi that builds upon joint work with Scott Taylor. (* Modulo a conjecture whose solution by Hanselman-Rasmussen-Watson has been announced.)

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: University of Miami

2018-01-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64470

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/