2004 Fiscal Year Final Research Report Summary
Study of analogies between algebraic number theory and 3-dimensional topology.
| Project/Area Number |
15540017
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kanazawa University |
|---|
Principal Investigator |
MORISHITA Masanori Kanazawa Univ., Dept.of Math., Associate Prof., 大学院・自然科学研究科, 助教授 (40242515)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KURIHARA Masato Tokyo Metro., Dept.of Math., Associate Prof., 理学部, 助教授 (40211221)
TAGUCHI Yuichiro Kyushu Univ., Dept.of Math., Associate Prof., 大学院・数理学研究院, 助教授 (90231399)
KOHNO Toshitake Tokyo Univ., Dept.of Math.Sci., Prof., 大学院・数理科学研究科, 教授 (80144111)
SUGANO Takashi Kanazawa Univ., Dept.of Math., Prof., 自然科学研究科, 教授 (30183841)
野村 明人 金沢大学, 自然科学研究科, 助教授 (00313700)
USHIJIMA Akira Kanazawa Univ., Dept.of Math., Lect. (50323803)
|
|---|
| Project Period (FY) |
2003 – 2004
|
| Keywords | prime / knot / number field / 3-manifold |
|---|
| Research Abstract |
I have worked on analogies between algebraic number theory and 3-dimensuonal topology, based on the analogy between primes and Knots. More precise results I obtained are as fellows.
1)I have pursued analogies between Iwasawa theory and Alexandev-Fox theory. In particular, I found that the relation between topological and analytical fusions is regarded as an analogue of the Iwasawa main Conjecture. giving the relation between algebraic Iwasawa polynomial and analytic p-adie L-functions. I have a research plan to pursue analogies in the context of geometry of Kato's Theory of zeta elements, the formulation of generalized Iwasawa main conjecture etc.
2)I have pursued analogies between the spaces of deformations of Galore representations and the character varieties of a knot group and found a certain analogy between the space of Hida's deformations and the She character variety of a hyperbolic knot group. I have a research plan to pursue analogies of 2-dimensional p-adie L-functions in the context of P of theory.
|
Research Products
(6 results)
