2001 Fiscal Year Final Research Report Summary
Research on Schottky spaces and Jorgensen groups
| Project/Area Number |
12640168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
SATO Hiroki Shizuoka University, Science Professor, 理学部, 教授 (40022222)
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| Co-Investigator(Kenkyū-buntansha) |
AKUTAGAWA Kazuo Shizuoka University, Science, Associate Professor, 理学部, 助教授 (80192920)
OKUMURA Yoshihide Shizuoka University, Science, Associated Professor, 理学部, 助教授 (90214080)
NAKANISHI Toshihiro Nagoya University, Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (00172354)
KUMURA Hironori Shizuoka University, Science, Lecturer, 理学部, 講師 (30283336)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Schottky space / Schottky group / Jorgensen group / Jorgensen's inequalitu / Kleinian group / hyperbolic space / Picard group / Whitehead link |
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| Research Abstract |
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.
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Research Products
(12 results)
