Research on Schottky spaces and Jorgensen groups

肖特基空间和乔根森群的研究

• 批准号: 12640168
• 负责人: SATO Hiroki
• 金额: $ 2.24万
• 依托单位: Shizuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640168/
• 关键词: Schottky space; Schottky group; Jorgensen group; Jorgensen's inequalitu; Kleinian group; hyperbolic space; Picard group; Whitehead link; リーマン面

We have studied the following four themes from 2000 to 2001. 1. Jorgensen groups. 2. Jorgensen numbers of Classical Schottky spaces of real type. 3. The Picard group. 4. The Whitehead link.1. J0rgensen groups. A Jorgensen group is a discrete group whose Jorgensen number is one. First we considered two one-parameter families. The results appeared in Contemporary Mathematics in 2000. Furthermore we studied Jorgensen groups of parabolic type. We talked the results at the Meeting of AMS (UCLA, 2000) and at the International Coference of Complex Analysis (China, 2000). Recently we found almost all Jorgensen groups of parabolic type. We talked about the results at the Meeting of Discontinuous Groups at Shizuoka University (January, 2002 and the Geometry and Topology Seminar at University of Oregon in March, 2002.2. Jorgensen numbers of Classical Schottky space of real type. We found the best lower bounds for all kinds of the classical Schottky spaces of real type. The results appeared in J. Math. Soc. Japan in 2001.3. The Picard group. We have appointed out before that the Picard group is a two-generator group. This time we constructed a new fundamental region for the group and we found eight relations by using the fundamental region. We talked this result at the ISAAC Congress in Berlin in 2001. The result will appear in the Proceedings.4. The Whitehead link. We proved that the Jorgensen number of the Whitehead link is two. Therefore the Whitehead link is not a Jorgensen group. We talked the result at Kyoto University in 2001. We will talk this result at the internatonal conference in 2002.

我们研究了从2000年到2001年的以下四个主题。1。jorgensen组。 2。真实类型的经典Schottky空间的Jorgensen数量。 3。皮卡德组。 4。链接1。 J0rgensen组。 Jorgensen组是一个离散的组，其Jorgensen数字是一个。首先，我们考虑了两个单参数家庭。结果出现在2000年的当代数学中。此外，我们研究了抛物线类型的Jorgensen群体。我们在AMS会议（UCLA，2000年）和国际复杂分析（Chine，2000年）的会议上讨论了结果。最近，我们发现了几乎所有的抛物线类型的Jorgensen组。我们谈到了Shizuoka University的不连续小组会议的结果（2002年1月，以及俄勒冈大学在俄勒冈大学举行的几何学和拓扑研讨会，2002.2。在这一次，我们为该小组建立了一个新的基本区域，我们在2001年在柏林的Isaac国会上进行了八个关系。京都大学于2001年。我们将在2002年的国际化会议上讨论这一结果。

项目成果

Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Proc. Eighth Inter. Conf. on Complex Analysis. 173-178 (2001)

Yoshihide Okumura：“提升问题及其在黎曼曲面上的应用”Proc。

Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Proc.Eighth International Conference on Complex Analysis. (2001)

Yoshihide Okumura：“提升问题及其在黎曼曲面上的应用”Proc.第八届国际复分析会议。

Kazuo Akutagawa: "An obstraction to the positivity of relative Yamabe invariants"Math. Z.. (to appear). (2002)

芥川一夫：“对相对山边不变量的积极性的阻碍”数学。

Hiroki Sato: "Jφrgensen's inequality for classical Schottky groups of real type, II"J.Math.Soc.Japan. 53. (2001)

Hiroki Sato：“实型经典肖特基群的 Jφrgensen 不等式，II”J.Math.Soc.Japan 53。（2001 年）

Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Proc.Eighth International Conference on Complex Analysis. 173-179 (2001)

Yoshihide Okumura：“提升问题及其在黎曼曲面上的应用”Proc.第八届国际复分析会议。