Analysis of deformation space of 3-dimensional cone-hyperbolic structures using fundamental domains arising from cut loci

使用切割轨迹产生的基本域分析 3 维锥双曲结构的变形空间

• 批准号: 20740043
• 负责人: AKIYOSHI Hirotaka
• 金额: $ 1.91万
• 依托单位: Kinki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740043/
• 关键词: 幾何学; トポロジー

The space of cone-hyperbolic structures for the 3-dimensional cone-manifold obtained as the product of the torus with a cone-point and the real line was studied in order to establish the deformation theory of 3-dimensional cone-hyperbolic structures for cone-manifolds with noncompact cone singularity. The deformation was studied by using a variant of Ford domains in the theory of Kleinian groups. A geometric parametrization for such space was established, which is conjectured to give a parametrization for certain slice of the character variety of one-holed torus defined by Tan et al. in terms of dynamics on the variety.

为了建立具有非紧锥奇性的锥流形的三维锥双曲结构的变形理论，研究了由圆锥与圆锥点和实直线的乘积得到的三维圆锥流形的锥双曲结构空间。用Kleian群理论中的Ford域的变体研究了这种形变。建立了该空间的几何参数化法，并对Tan等人定义的单孔环面特征变量的某些切片进行了参数化。就品种的动态而言。

项目成果

Side Parameter for the Punctured Torus Groups

穿孔环面组的侧面参数

• 发表时间: 2009
• 期刊: Proceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
• 作者: 庄田敏宏;庄田敏宏;庄田敏宏;庄田敏宏;Hirtotaka Akiyoshi
• 通讯作者: Hirtotaka Akiyoshi

Side parameter for the pullctured torus groups

拉伸环面组的侧面参数

• 发表时间: 2008
• 作者: 庄田敏宏;庄田敏宏;庄田敏宏;庄田敏宏;Hirtotaka Akiyoshi;Hirtotaka Akiyoshi;秋吉宏尚;秋吉宏尚
• 通讯作者: 秋吉宏尚