2006 Fiscal Year Final Research Report Summary
Stady of Arithmcfc Topology
| Project/Area Number |
17540020
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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 |
Algebra
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| Research Institution | KYUSHU UNIVERCITY |
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Principal Investigator |
MORISHITA Masanori Kyushu University, Faculty of Mathematics, Professor, 大学院数理学研究院, 教授 (40242515)
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| Co-Investigator(Kenkyū-buntansha) |
TAGUCHI Yushiro Kyushu University, Faculty of Mathematics, Associate Professor, 大学院数理学研究院, 助教授 (90231399)
KANHARA Masato Keio University, Faculty of Science, Professor, 理工学部, 教授 (40211221)
FUJII Michihiko Kyoto University, Faculty of Science, Associate Professor, 大学院理工研究科, 助教授 (60254231)
TERASHMA Yuji Tokyo Institute Technology, Faculty of Science, Assistant, 大学院理工学研究科, 助手 (70361764)
KOHNO Toshtake University of Tokyo, Faculfy of Mathematical Science, 大学院数理科学研究科, 教授 (80144111)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Knots / Primes |
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| Research Abstract |
Based on analogies between knots and primes, I investigated the connection and interaction between knot theory and number theory. In this year, my concern has been focused on the following topics :
I showed the analogy between the structure of the deformation space of hyperbolise structures on a knot complement and the deformation space of p-adic Galvis representations of a prime group. Based on this analogy, I discussed some analogous features between the variation of Sh_2(C) Chern-Simons. in variants and p-adre modulus L-function. In particular, I gave an interpretation of the Chern-Simons invariant in terms of Deligne cohomology, Jointly with Y.Terashima. I talked about Dnr results in the international conferees hold at Hiroshima Univ.(2006,July), Max Plank Inst.(2006,Sept) and Kyoto Un.(2006,Dec)
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