Heegaad splittings of 3-dimensional manifolds and geometric structures

3 维流形和几何结构的 Heegaad 分裂

• 批准号: 12440018
• 负责人: NAMBA Makoto
• 金额: $ 9.41万
• 依托单位: OSAKA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440018/
• 关键词: fundamental group; finite Galois coverings; Zariski pair; hyperbolic manifolds; punctured torus; Epstein-Penner docomposition; McShane's indentity; quasifuchisian space; 双曲空間; 3次元多様体; ヘガード分解; 擬フックス群; フォード領域; 有限分岐被覆; 退化族; カスプ付き双曲多様体; 理想多面体分

(1)Fundamental groups and branched coverings. M.Namba gave with H.Tsuchihashi a method for concrete computations of fundamental groups of the compliments of curves in the complex projective plane and finite branched Galois coverings branching along the curves, and gave a new example of Zariski pair using the method.(2)Generaliztion of Epsein-Penner decomposition. H.Akiyoshi and M.Sakuma gave a generalization of the Epstein-Penner decompositions of cusped hyperbol manifolds of finite volume to those of infinite volume, and studied relation with the convex cores. They collaborated with M.Wada and Y.Yamashita and gave partial answer and experimental evidences to their conjecture that the pleating loci would determine the generalized Epstein-Pener decompositions for punctured torus groups.(3)H.Akiyoshi, M.Miyachi and M.Sakuma have established a variation of McShane's identity for punctued surface bundles over a circle, which expresses the modulus of cusptori in terms of the complex translation lengths of essential simple loops of the fiber surfaces.(4)Drawing the 3D slices of the quasifuchsian punctured torus space. M.Wada and Y.Yamashita developed a software to draw (real) 3-dimensional slices of the quasifuchsian punctured torus space

（1）基本组和分支覆盖物。 M.Namba用H.Tsuchihashi给出了一种方法，用于计算复杂的投影平面中曲线的基本组和沿曲线分支有限的分支的Galois覆盖物，并使用该方法给出了Zariski对的新示例。（2）Epsein-Penner分解的概括。 H.akiyoshi和M.Sakuma对有限体积的cus倍倍歧管的Epstein-Penner分解对无限体积的分解进行了概括，并研究了与凸内核的关系。他们与M.Wada和Y.Yamashita合作，并给出了部分答案和实验证据，表明他们的猜想将确定pleating pleating loci的基因座的普遍化的爱泼斯坦 - 派台 - 刺穿的圆环组。（3）H.Akiyoshi，M.Miyyachi和M.Miyyachi和M.Sakuma的表面概况均可构想，同时表达了一定的范围，同时又有一定的循环范围。在纤维表面必需简单环的复杂翻译长度方面。 M.Wada和Y.Yamashita开发了一种软件，用于绘制（真实的）三维切片的刺穿圆环空间

项目成果

H.Akiyoshi, M.Sakuma: "Comparing two convex hull constructions of cusped hyperbolic manifolds"London Mathematical Society Lec.Notes. 299. 209-246 (2003)

H.Akiyoshi、M.Sakuma：“比较尖点双曲流形的两种凸包结构”伦敦数学会 Lec.Notes。

H.Akiyoshi, M.Sakuma: "Comparing two convex hull constructions of cusped hyperbolic manifolds"To appear in Proc.Workshop "Kleinian groups and hyperbolic 3-manifolds". London M.Soc.Lec.N.. (2002)

H.Akiyoshi、M.Sakuma：“比较尖点双曲流形的两种凸包结构”出现在 Proc.Workshop“Kleinian 群和双曲 3-流形”中。

H.Akiyoshi, M.Skuma: "Comparing two convex hull constructions for cusped hyperbolic manifolds"London Math.Society Lec.Notes. 299. 209-246 (2003)

H.Akiyoshi、M.Skuma：“比较尖双曲流形的两种凸包结构”伦敦数学学会讲座笔记。

村上 順: "The colored Jones polynomials and the simplicial volume of a knot"Acta Math.. 186. 85-104 (2001)

Jun Murakami：“彩色琼斯多项式和结的单纯体积”Acta Math.. 186. 85-104 (2001)

T.Kobayashi: "Scharlemann-Thompson untelescoping of Heegaard splittings is finer than Casson-Gordon's"J.Knot Theory Ramifications. 12. 877-891 (2003)

T.Kobayashi：“Scharlemann-Thompson 对 Heegaard 分裂的解伸缩比 Casson-Gordon 的”J.Knot 理论分支更好。