Handlebody splittings of 3-manifolds with bounday

带边界的 3 歧管手柄体分裂

• 批准号: 10640094
• 负责人: SUZUKI Shinichi
• 金额: $ 0.58万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640094/
• 关键词: 3-manifolds; Heegaard splittings; handlebodies; 3次元多様体; ハンドル体分解; Heegaard分解

We call a compact, connected, orientable 3-manifold M with nonempty boundary ∂M a bordered 3-manifold. A bordered 3-manifold H is said to be a handlebody of genus g iff H is the disk-sum (= the boundary connected-sum) of g copies of the solid-torus.It is well-known that a closed (=compact, without boundary) , connected, orientable 3-manifold M is decomposed into two homeomorphic handlebodies ; and such a splitting is called a Heegaard splitting for M.On the other hand, in 1970 J. S. Downig proved that every bordered 3-manifold can be decomposed into two homeomorphic handlebodies, and L. G. Roeling discoursed on these decompositions for bordered 3-manifolds with connected boundary. The research results are (1) to report the Downing's results in slightly modified forms, (2) to generalize the Roeling's results to borderd 3-manifolds with several boundaries, (3) to formulate a Haken type theorem for these decompositions in the way of Casson and Gordon, and (4) to discuss another Haken type theorem for these decomposition with essential proper disks.

我们称一个紧的，连通的，可定向的具有非空边界∂M的3流形M为有边界的3流形。一个有边界的3流形H被称为g属的柄体，如果H是固体环面的g个拷贝的盘和（=边界连通和）。众所周知，一个闭合的（紧的，无边界的），连通的，可定向的3-流形M被分解成两个同胚的柄体；另一方面，j.s. Downig在1970年证明了每一个有边3流形都可以分解为两个同胚柄体，L. G. Roeling讨论了具有连通边界的有边3流形的分解。研究结果有：(1)以稍作修改的形式报道了Downing的结果；(2)将Roeling的结果推广到具有多个边界的有边3流形；(3)用Casson和Gordon的方法给出了这些分解的一个Haken型定理；(4)讨论了这些分解的另一个带本质固有盘的Haken型定理。

项目成果

Shin'ichi Suzuki: "Handlebody splittings of compact 3-manifolds with boundary"Proceedings of Workshop Knots 1999,. (2000)

Shinichi Suzuki：“带有边界的紧凑 3 歧管的手柄体分裂”，Workshop Knots 1999 年论文集，。

Shin'ichi Suzuki: "Handlebody splittings of compact 3-manifolds with boundary"Proceedings "Knot Theory" (ed. M. Sakuma). 323-330 (2000)

Shinichi Suzuki：“带边界的紧凑 3 流形的手柄体分裂”论文集“结理论”（M. Sakuma 编辑）。

Shinichi Suzuki: "Handlebody splittings of compact 3-manifolds with boundary"Proceedings of Workshop Knots Theory 1999, ed. M. Sakuma. 323-330 (2000)

Shinichi Suzuki：“带边界的紧凑 3 流形的手柄体分裂”Proceedings of Workshop Knots Theory 1999，编辑。

鈴木晋一: "コンパクト境界付き3次元多様体のハンドル体分解" 早稲田大学教育学部学術研究(数学編). 46号. (1998)

铃木真一：“处理紧有界3维流形的场分解”早稻田大学教育学部学术研究（数学版）第46期。（1998年）。