Representation spaces, Teichmüller theory, and their relationship with 3-manifolds from the classical and quantum viewpoints / Espaces de représentations, théorie de Teichmüller et leur rapport avec les 3-variétés d'un point de vue classique et quantique

Collection Representation spaces, Teichmüller theory, and their relationship with 3-manifolds from the classical and quantum viewpoints / Espaces de représentations, théorie de Teichmüller et leur rapport avec les 3-variétés d'un point de vue classique et quantique

Organizer(s) Boileau, Michel ; Kitano, Teruaki ; Morifuji, Takayuki ; Paoluzzi, Luisa

Date(s) 29/01/2018 - 02/02/2018

linked URL https://conferences.cirm-math.fr/1891.html

00:00:00 / 00:00:00

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L-space knots in twist families and satellite L-space knots

By Kimihiko Motegi

Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots ${K_n}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n) \to 1$ as $n \to \infty$, then either the winding number of $K$ about $c$ is zero or the winding number equals the wrapping number. As an application, if ${K_n}$ contains infinitely many L-space knots, then the latter must occur. We further develop this to show that if $K_n$ is an L-space knot for infinitely many integers $n > 0$ and infinitely many integers $n < 0$, then $c$ is a braid axis. We then use this to show that satellite L-space knots are braided satellites. This is joint work with Ken Baker.

Information about the video

Date of recording 31/01/2018
Date of publication 07/02/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19273003
Cite this video Motegi, Kimihiko (31/01/2018). L-space knots in twist families and satellite L-space knots. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19273003
URL https://dx.doi.org/10.24350/CIRM.V.19273003

Domain(s)

Geometric Topology

Bibliography

Baker, K.L., & Motegi, K. (2017). Twist families of L-space knots, their genera, and Seifert surgeries. <arXiv:1506.04455> - https://arxiv.org/abs/1506.04455

MSC codes

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