Studies on Combinatorial Structures of 3-Manifolds

3-流形组合结构的研究

• 批准号: 10640089
• 负责人: ISHII Ippei
• 金额: $ 0.9万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640089/
• 关键词: 3-manifold; spine; Heegaard splitting; Dehn surgery; Poincare conjecture; 三次元多様体; ヘゴール分解; Heegaard分解; framed link; Dehn手術; spine; DS-deagram

(1) On Ds-diagramsIt was shown that two Ds-diagrams representing the same closed 3-manifold can be transformed to each other by a sequence of "elementary deformations".(2) On Heegaard splittingsA new condition for a Heegaard splitting to be reducible has been found. This condition is described by the notion of a "d-pseudo core".(3) On framed links in a homotopy 3-sphereIt was shown that any homotopy 3-sphere admits a "very special framed link" , which enjoys a good property and closely related to a Heegaard splitting.(4) On the Poincare conjectureUsing the above two results (2) and (3), we have proposed a new method for attacking the famous "Poincare conjecture".

(1)关于Ds图表明，代表同一封闭3流形的两个Ds图可以通过一系列“基本变形”相互变换。(2)关于Heegaard分裂Heegaard分裂可约化的新条件已经被发现。这个条件用“d-伪核”的概念来描述。(3)关于同伦3-球中的框架链接表明，任何同伦3-球都承认一个“非常特殊的框架链接”，它具有良好的性质，并且与赫加德分裂密切相关。(4)关于庞加莱猜想利用上述两个结果(2)和(3)，我们提出了一种攻击著名的“庞加莱猜想”的新方法。 推测”。

项目成果

I.Ishii: "Very special framed links for a homotopy 3-sphere"Tokyo J.Math.. (to appear).

I.Ishii：“同伦 3 球体的非常特殊的框架链接”Tokyo J.Math..（即将出现）。

H. Enomoto: "Connecte Sabgraphs with Small Subgraphs with Small Degree sums in 3-connected Plane Graphs"J. Graph Theory. (to appear).

H. Enomoto：“在 3 连通平面图中将 Sabgraphs 与具有小度数和的小子图连接起来”J。

I. Ishii: "A new condition for a Heegaard spliffine to be reductable"Tokyo J. Math.. (to appear).

I. Ishii：“Heegaard spliffine 可还原的新条件”Tokyo J. Math..（出现）。

H.Enomoto: "Connecte Subgraphs with Small Subgrophs with Small Degres Su*s in 3-connected planer Graphs"J.Groph Theory. (to appear).

H.Enomoto：“在 3 连通平面图中将子图与小子图与小度数 Su*s 连接起来”J.Groph 理论。

H.Omori: "Noncommutative 3-sphere"J.Math.Soc.Japan. 50. 915-943 (1998)

H.Omori：“非交换 3 球”J.Math.Soc.Japan。