Representations of 3-manifolds and geometric informations derived from them

3-流形的表示以及从它们导出的几何信息

• 批准号: 12640071
• 负责人: KOBAYASHI Tsuyoshi
• 金额: $ 1.79万
• 依托单位: Nara Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640071/
• 关键词: Heegaard splitting; 3-manifold; knot; Tunnel number; Dehn twist; Ricci curvature; Einstein metric; Heegaard Splitting; Untelescoping; 3-manifold; Knot; knot; triangulation

1. Graphic of 3-manifoldsKobayashi make use of the graphic defined by Rubinstein-Scharlemann to give a complete classification of Heegaard splittings of the exteriors of the 2-bridge knots.2. Local detection of strong irreducibility of Heegaard splittings by using knot exteriorsKobayashi together with, Yo'av Rieck analyzed how strongly irreducible Heegaard splittings can intersect the exteriors of non-trivial knots in the 3-sphere and showed that such Heegaard surface intersect the knot exteriors in meridional annuli.3. Research on Morimoto's ConjectureKobayashi together with Yo'av Rieckstudied about Morimoto's Conjecture concerned with the connectedsums of knots in 3-manifolds and the tunnel numbers.4. Algorithm for decompositions of attaching homeomorphisms of Heegaard splittings into Dehn twistsOchiai gave an algorithm for giving a decomposition of given attaching homeomorphisms of genus two Heegaard splittings into standard Dehn twists.5. Moduli space of metrics of Riemannian manifoldsKatagiri studied about Riemannian functional via Ricci curvature and showed that Einstein metric is a critical point of this functional, however there exist critical points that are not Einstein metric. He also gave a sufficient condition for critical points to be Einstein metrics.

1. 3流形的图解Kobayashi利用Rubinstein-Scharlemann定义的图解给出了2-桥结外部的Heegaard分裂的完整分类. Kobayashi和Yo'av Rieck分析了强不可约Heegaard分裂如何与三维球面中的非平凡纽结的外部相交，并证明了这种Heegaard曲面与三维球面中的纽结外部相交. Morimoto猜想的研究Kobayashi和Yo'av Rieck研究了与三维流形中纽结的连通和隧道数有关的Morimoto猜想.将Heegaard分裂的附加同胚分解为Dehn扭转的算法Ochiai给出了将亏格为两个Heegaard分裂的给定附加同胚分解为标准Dehn扭转的算法。5. Katagiri利用Ricci曲率研究了黎曼泛函，证明了Einstein度量是该泛函的一个临界点，但存在非Einstein度量的临界点.他还给出了临界点是爱因斯坦度量的充分条件。

项目成果

T.Kobayashi: "Heegaard splittings of exteriors of two bridge knots"Geometry and Topology. 5. 609-650 (2001)

T.Kobayashi：“两个桥结外部的 Heegaard 分裂”几何与拓扑。

M.Hirasawa, T.Kobayashi: "Pre-taut sutured manifolds and essential laminations"Osaka J.Math.. 38. 905-922 (2001)

M.Hirasawa、T.Kobayashi：“预拉紧缝合歧管和基本叠片”Osaka J.Math.. 38. 905-922 (2001)

Tsuyoshi Kobayashi: "Heegaard splitting of exteriors of two bridge knots"Geometry and Topology. 5. 609-650 (2001)

Tsuyoshi Kobayashi：“两个桥结外部的 Heegaard 分裂”几何与拓扑。

Mitsuyuki Ochiai: "Computational Decomposition of Homeomorphisms of Planar Heegaard Diagrams"Far East J.Math.Sci.. 2. 869-895 (2001)

Mitsuyuki Ochiai：“平面 Heegaard 图同态的计算分解”Far East J.Math.Sci.. 2. 869-895 (2001)

M.Ochiai: "Non-iterative行列演算による3次元空間における曲面の最適埋蔵法"情報処理学会論文誌. (to appear).

M.Ochiai：“使用非迭代矩阵运算的三维空间中曲面的最佳嵌入方法”，日本信息处理学会会刊（待发表）。