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.

双曲线结上的Seifert手术是如何由圆环结上的？我们从网络观点来解决这个问题。我们的基本思想是使用Seiferter的``遗传''特性找到此类手术之间的关系。从一个Seifert手术到另一种的网络中的一条路径，解释了如何从后者那里从后者获得了以前的Seifert手术，沿着Seiferters的一系列扭曲和/或Annuli的大多数Suifers surous of Seifits pairs of Seifers seruls of Seifers seruls of Seifers seruls of Seifers seruls of seifers。经过良好的塞夫手术。

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

Seifert fibered surgeries without primitive/Seifert positions having their origins in those on a trefoil knot

没有原始/Seifert位置的Seifert纤维手术起源于三叶结上的位置

• 发表时间: 2012
• 作者: Jorg Schtlrmann;Shoji Yokura;Kazuo Akutagawa;小池直之;中川征樹;陶山芳彦;高倉樹;陶山芳彦;K.Motegi;中川征樹;Takehiko Yasuda;Kazuo Akutagawa;小池直之;陶山芳彦;三好重明;中川征樹;茂手木公彦;田丸博士;Kazuo Akutagawa;Takehiko Yasuda;高倉樹;中川征樹;K.Motegi;小池直之;Tadashi Aikou;Yoshihiro Tonegawa;高倉樹;Tadashi Aikou;茂手木公彦
• 通讯作者: 茂手木公彦