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.

双曲线结的 Seifert 手术与环面结的手术有何不同？我们从网络的角度来解决这个问题。我们的基本想法是利用 Seifert 的“继承”特性来寻找此类手术之间的关系。网络中从一个 Seifert 手术到另一个 Seifert 手术的路径解释了前一个 Seifert 手术是如何在沿着 Seifert 和/或一系列扭曲之后从后者获得的。我们发现了从各种已知的 Seifert 手术到环面结（最基本且易于理解的 Seifert 手术）的明确路径。沿着“双曲塞弗特”或“双曲环形对”在双曲结上产生无限多个塞弗特手术我们给出了对具有双曲塞弗特或双曲环形对的环面结的塞弗特手术列表，并获得了表明这样的结果。手术受到限制。

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

• 发表时间: 2013
• 作者: K.Motegi

Seifert surgeries on knots and their network

塞弗特对结及其网络进行的手术

• 发表时间: 2009
• 作者: K.Motegi

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

• 作者: Kimihiko Motegi

Networking Seifert surgeries on knots: a survey and problems

网络 Seifert 结手术：调查和问题

• 作者: 茂手木公彦

Band sum operations yielding trivial knots

带和运算产生琐碎的结

• 发表时间: 2009
• 作者: K.Ishihara; K.Motegi
• 通讯作者: K.Motegi