Networking Seifert surgeries on knots

网络 Seifert 结手术

• 批准号: 21540098
• 负责人: MOTEGI Kimihiko
• 金额: $ 2.75万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540098/
• 关键词: 幾何学; トポロジー; 結び目; ３次元多様体; Dehn手術; Seifert fiber space; seiferter; Seifert Surgery Network; Dehn surgery; lens space; hyperbolic knot; closed geodesic; band sum

How do Seifert surgeries on hyperbolic knots arise from those on torus knots? We approach this question from a networking viewpoint. Our basic idea is finding relationships among such surgeries using ``inheritance" property of seiferters. A path in the network from one Seifert surgery to another explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. We find explicit paths from various known Seifert surgeries to those on torus knots, the most basic and well-understood Seifert surgeries. Successive twists along a ``hyperbolic seiferter" or a ``hyperbolic annular pair" produce infinitely many Seifert surgeries on hyperbolic knots. We have given a list of Seifert surgeries on torus knots which have hyperbolic seiferters or hyperbolic annular pairs, and obtained results suggesting that such surgeries are restricted.

如何塞弗特手术双曲结产生的环面结？我们从网络的角度来探讨这个问题。我们的基本思想是利用seiferters的“继承”性质来发现这些手术之间的关系。从一个塞弗特手术到另一个的网络中的路径解释了前塞弗特手术是如何从后者获得后，一系列的扭曲沿着塞弗特和/或环cobounded对塞弗特。我们发现明确的路径，从各种已知的塞弗特手术的环面结，最基本的和众所周知的塞弗特手术。连续的扭曲沿着一个“双曲塞弗特”或一个"双曲环形对”产生无限多个塞弗特手术双曲结。我们已经给出了一个列表的塞弗特手术环面结双曲塞弗特或双曲环形对，并获得的结果表明，这种手术是有限的。

项目成果

Seifert fibered surgeries on strongly invertible knots without primitive/Seifert positions

在没有原始/Seifert 位置的强可逆结上进行 Seifert 纤维手术

• DOI: 10.1016/j.topol.2015.05.016
• 发表时间: 2015
• 期刊: Topology Appl.
• 作者: Mario Eudave-Munoz;Edgar Jasso;Katura Miyazaki and Kimihiko Motegi
• 通讯作者: Katura Miyazaki and Kimihiko Motegi

Seifert surgery network and chain links

Seifert手术网络和链环

• 发表时间: 2013
• 作者: T.Suzuki;T.Takakura;Takehiko Yasuda;K.Motegi
• 通讯作者: K.Motegi

Kimihiko MOTEGI's Home Page

茂木公彦的主页

Networking Seifert surgeries on knots II : Berge's lens surgeries

纽结 II 上的网络 Seifert 手术：Berge 的晶状体手术

• 发表时间: 2009
• 期刊: Topology Appl 156
• 作者: A. Deruelle;K. Miyazaki and K. Motegi
• 通讯作者: K. Miyazaki and K. Motegi

Networking Seifert surgeries on knots III

网络结 III 上的 Seifert 手术

• 发表时间: 2014
• 期刊: Algebr. Geom. Topol.
• 作者: Arnaud Deruelle;Katura Miyazaki;Kimihiko Motegi
• 通讯作者: Kimihiko Motegi