Heegaard structures and geometric structures of 3-manifolds

Heegaard 结构和 3 流形的几何结构

• 批准号: 18340018
• 负责人: SAKUMA Makoto
• 金额: $ 6.34万
• 依托单位: Hiroshima University (2007-2009)Osaka University (2006)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340018/
• 关键词: 3次元多様体; ヘガード分解; 幾何構造; 双曲構造; 穴あきトーラス; 曲面束; Cannon-Thurston map; 標準的分割; 2橋結び目; small cancellation theory; へガード分解; Cannon-Thurston写像; Canonical decomposition; Cannon-Thurston-Dicks分解; 穴あきトーラス束; 強可逆結び目; 垣水複体; Montesinos knot; virtual fiber /

We have concentrated on the study of the once-punctured torus, the simplest hyperbolic surface, believing that it would bring us to deep understanding of general hyperbolic surfaces, and obtained the following results. (1) We gave a complete description and proof to Jorgensen's theory on quasifuchsian punctured torus groups. (2) We found an intimate relation between the following two tessellations associated with a punctured torus bundles over the circle ; the Cannon-Thurston-Dicks fractal tessellation and the cusp triangulation induced by the canionical decomposition. We also proposed a conjecture concerning the canonical decompositions of punctured surface bundles over the circle. (3) We gave a complete characterization of those essential simple loops on the bridge sphere of a 2-bridge knot which are null-homotopic in the knot complement.

我们集中研究了最简单的双曲曲面——曾经刺穿的环面，相信这将加深我们对一般双曲曲面的理解，并得到了以下结果。 (1)我们对Jorgensen的拟福赫斯穿孔环面群理论给出了完整的描述和证明。 (2) 我们发现以下两个镶嵌图案之间存在密切关系，这些镶嵌图案与圆上的穿孔环面束相关； Cannon-Thurston-Dicks 分形镶嵌和正则分解引起的尖点三角剖分。我们还提出了关于圆上穿刺面束的正则分解的猜想。 (3) 我们对 2 桥结的桥球上的那些基本简单环给出了完整的表征，这些简单环在结补中是零同伦的。

项目成果

Spaces of Kleinian groups

• DOI: 10.1007/bfb0060314
• 发表时间: 1970
• 作者: L. Bers

Epimorphisms among 2-bridge knot groups from the view point of markoff maps, Intelligence of low dimensional topology 2006

从markoff图的角度看2桥结群的同态，低维拓扑智能2006

• 发表时间: 2007
• 期刊: World Scientific ( J. Scott carter, etal)
• 作者: 高野曉;服部裕司;金元敏明;Makoto Sakuma
• 通讯作者: Makoto Sakuma

Epimorphisms among 2-bridge knot groups and end invariants of SL(2, C)-representations

2 桥结群之间的同态和 SL(2, C) 表示的末端不变量

• 发表时间: 2009
• 作者: K.Momihara;M.Jimbo;津田一郎;T. Ito;Makoto Sakuma
• 通讯作者: Makoto Sakuma

The spaces of Kleinian groups and hyperbolic 3-manifolds

克莱因群和双曲 3-流形的空间

• 发表时间: 2006
• 作者: Yaiir Minsky;Makoto Sakuma;Caroline Series (eds)
• 通讯作者: Caroline Series (eds)

Variations of Mcshanes indentify for punctured surface groups

Mcshanes 的变体识别穿孔表面组

• 发表时间: 2006
• 期刊: London Math. Soc. Lect. Notes Series 329
• 作者: H.Akiyoshi;H.Miyachi;H.Sakuma
• 通讯作者: H.Sakuma