2003 Fiscal Year Final Research Report Summary
Research on discrete groups and profective strucutures on Riemann surfaces
| Project/Area Number |
13440045
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Nagoya University |
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Principal Investigator |
NAKANISHI Toshihiro Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (00172354)
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| Co-Investigator(Kenkyū-buntansha) |
OHOSHIKA Ken'ichi Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70183225)
SATO Hiroki Shizuoka University, Faculty of Science, Professor, 理学部, 教授 (40022222)
SHIGA Hiroshige Tokyo Institute of Technology, Graduate School of Science and Technology, Professor, 大学院・理工学研究科, 教授 (10154189)
FUJII Michihiko Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (60254231)
TANIGUCHI Masahiko Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Riemann surface / Kleinian group / hyperbolic geometry / low dimensional manifold / projective structure |
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| Research Abstract |
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.
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