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-流形图小林利用Rubinstein-Scharlemann定义的图给出了2-桥结外部Heegaard分裂的完整分类。2．使用结外部局部检测 Heegaard 分裂的强不可约性Kobayashi 与 Yo'av Rieck 一起分析了不可约 Heegaard 分裂与 3 球体中非平凡结的外部相交的强度，并表明这样的 Heegaard 表面与结外部相交子午环.3.森本猜想的研究小林与Yo'av Rieck一起研究了有关3流形结连通和及隧道数的森本猜想。 4． Heegaard分裂的附着同态分解为Dehn扭曲的算法Ochiai给出了一种将属二Heegaard分裂的附着同态分解为标准Dehn扭曲的算法。 5．黎曼流形度量模空间Katagiri通过Ricci曲率研究了黎曼泛函，并表明爱因斯坦度量是该泛函的临界点，但也存在非爱因斯坦度量的临界点。他还给出了临界点成为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.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）。

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)

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

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