Hecguard Splittings and genetic structures of 3-manifolds

Hecguard 分裂和 3 流形的遗传结构

• 批准号: 14340023
• 负责人: SAKUMA Makoto
• 金额: $ 6.98万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340023/
• 关键词: quasi-fuchsian group; punctured torus; Hecguard Splittings; Ford domain; 2-bridge knot; 穴開トーラス; 錐多様体; McShaneの等式; ザイフェルト曲面; 穴開きトーラス群; Weil-Petersson距離; 極限集合; 双曲結び目; カスプ; 曲面束; 穴あきトーラス; 双曲構造

The main results obtained by this project are as follows.1.Akiyoshi, Sakuma, Wada and Yamashita have completed a preprint (256 pages) which gives a full exposition of Jorgensen's theory for the Ford domains of quasifuchsian punctured torus groups, including a full proof. We plan to write a sequel of the paper to explain our extension of his theory to the outside of the quasifuchsian punctured torus space and to explain the relationship between the bridge structure of a 2-bridge knot and the complete hyperbolic structure of its complement.2.Epstein-Penner has introduced the Euclidean decompositions of finite-volume cusped hyperbolic manifolds through a convex hull construction in the Minkowski space. Akiyoshi-Sakuma has generalized the construction to (possibly) infinite-volume cusped hyperbolic manifolds and introduced EPH-decompositions of these manifolds. Moreover, relation between the EPH-decompositions and the bending laminations of cusped hyper-bolic manifolds were studied by Akiyoshi-Sakuma-Wada Yamashita.3.Akiyoshi-Miyachi-Sakuma have generalized Bowditch's variation of McShane's identity for hyperbolic punctured torus bundles to general hyperbolic punctured surface bundles.

本项目的主要结果如下：1. Akiyoshi，Sakuma，Wada和Yamashita完成了一份预印本（256页），全面阐述了Jorgensen关于拟Fuchsian穿孔环面群的福特域的理论，并给出了完整的证明。我们计划写一个续集的文件，以解释我们的扩展，他的理论以外的拟fuchsian穿孔环面空间，并解释之间的关系的桥梁结构的2桥结和完整的双曲结构的补充。2.Epstein-Penner通过一个凸船体建设的Minkowski空间中引入了有限体积尖双曲流形的欧氏分解。Akiyoshi-Sakuma将这种构造推广到（可能）无限体积尖点双曲流形，并引入了这些流形的EPH-分解。Akiyoshi-Miyachi-Sakuma将双曲穿孔环面丛的McShane恒等式的Bowditch变分推广到一般双曲穿孔曲面丛。

项目成果

A refinement of McShane's identity for quanguchsian punctures tones groups

McShane 对 quaguchsian 穿刺音组身份的改进

• 发表时间: 2004
• 期刊: Contemp. Math, Amer. Math. Soc. 40
• 作者: T.Kitano;M.Suzuki;M.Wada;K.Ohshika;K.Ohshika;M.Sakuma
• 通讯作者: M.Sakuma

H.Akiyoshi, M.Sakuma, M.Wada, Y.Yamashita: "Jorgensen's picture of quasifuchsian punctured torus groups"London Math Soc Lecture Note Series. 299. 247-273 (2003)

H.Akiyoshi、M.Sakuma、M.Wada、Y.Yamashita：“Jorgensen 的拟福赫斯穿孔环面群的图片”伦敦数学学会讲义系列。

Complexification of Lambda Length as Parameter for SL(2,C)-Rep. Space of Punctured Surface Groups

Lambda 长度的复数作为 SL(2,C)-Rep 的参数。

• 发表时间: 2004
• 期刊: J.London Math Soc. 70,2
• 作者: T.Nakanishi;M.Naatanen
• 通讯作者: M.Naatanen

Comparing two convex hull constructions of cusped hyperbolic manifolds

比较尖点双曲流形的两种凸包结构

• 发表时间: 2003
• 期刊: London Math.Soc.Lect.Note Series 299
• 作者: H.Akiyoshi;M.Sakuma
• 通讯作者: M.Sakuma

Teichmuller spaces of once-punctured tori

一次刺穿环面的 Teichmuller 空间

• 期刊: Experimental Math. (To appear)
• 作者: KOMORI;Yohei
• 通讯作者: Yohei