Research on discrete groups and profective strucutures on Riemann surfaces

黎曼曲面离散群及有效结构研究

• 批准号: 13440045
• 负责人: NAKANISHI Toshihiro
• 金额: $ 4.93万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440045/
• 关键词: Riemann surface; Kleinian group; hyperbolic geometry; low dimensional manifold; projective structure

A coordinate-system called lambda lengths is constructed for the SL(2,C) representation space of punctured surface groups. These lambda lengths can be considered as complexification of R.C.Penner's lambda lengths for decorated Teichmuller spaces. Via the coordinates the mapping class group acts on the representation space as a group of rational representations. We apply this fact to find hyperbolic 3-manifolds which fiber over the circle.

为刺破表面组的SL（2，c）表示空间构建了一个称为lambda长度的坐标系统。这些lambda长度可被视为用于装饰的Teichmuller空间的R.C. Penner的Lambda长度的复杂化。通过坐标，映射类组在表示空间上作为一组理性表示。我们应用这一事实来找到双曲线的三元纤维，这些纤维在整个圆圈上。

项目成果

M.Fuji, H.Ochiai: "An algorithm for solving linear ordinary differential equations of Fuchsian type with three singular points"Interdisciplinary Information Science. 9. 189-200 (2003)

M.Fuji，H.Ochiai：“求解具有三个奇异点的 Fuchsian 型线性常微分方程的算法”跨学科信息科学。

中西 敏浩: "λ-lengthの複素化について"数理解析研究所講究録. 1223. 50-55 (2001)

Toshihiro Nakanishi：“关于 λ 长度的复数”数学分析研究所的 Kokyuroku。1223. 50-55 (2001)。

Hiroshige Shiga: "On holomorphic families of rational maps : finiteness, rigidity and stability"Kodai Math. J.. 24. 48-65 (2001)

Hiroshige Shiga：“论有理图的全纯族：有限性、刚性和稳定性”Kodai Math。

Nayatani, S., H.Kamada: "Quaternionic analogue of CR geometry"Seminaire Theor. Spectral Geom.. 19. 41-52 (2001)

Nayatani, S., H.Kamada：“CR 几何的四元模拟”研讨会理论。

Fujii, M., H.Ochiai: "An algorithm for solving linear ordinary differential equations of Fuchsian type with three singular points"Interdisciplinary Information Sciences. 9. 189-200 (2003)

Fujii, M., H.Ochiai：“一种求解具有三个奇异点的 Fuchsian 型线性常微分方程的算法”跨学科信息科学。