2002 Fiscal Year Final Research Report Summary
Topology related to invariants of knots and 3-manifolds
| Project/Area Number |
13640064
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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 |
Geometry
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| Research Institution | The University of Tokyo (2002)
Tokyo Institute of Technology (2001) |
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Principal Investigator |
OHTSUKI Tomotada The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (50223871)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Kyoji Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究科, 教授 (20012445)
MURAKAMI Jun Waseda Univercity, Science and Engineering, Professor, 理工学部, 教授 (90157751)
MURAKAMI Hitoshi Tokyo Institute of Technology, Graduate School of Science and Engineering, Associate Professor, 大学院・理工学研究科, 助教授 (70192771)
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| Project Period (FY) |
2001 – 2002
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| Keywords | knot / 3-manifold / invariant |
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| Research Abstract |
By the support of the grant-in-aid I organized the workshop and seminars "Invariants of Knots and 3-Manifolds" at the Research Institute for Mathematical Sciences (RIMS), Kyoto University in September 2001, as activities of the 2001 RIMS research project "Low-Dimensional Topology in the Twenty-First Century". We had 70 domestic participants and 26 foreign participants.
Historically speaking, this research area is a relatively new area based on the enormous number of invariants, called quantum invariants, of knots and 3-manifolds, which have been derived from the Chern-Simons field theory in the 1980s. I think the topological reconstruction of these invariants has almost been completed by various works of these decades.
An aim of the workshop and seminars was to discuss future directions for this area.
To discuss these matters fully, I planned 1 month of activities, relatively longer than usual.
Further, to encourage discussions among the participants, we arranged a short problem session after each talk, and requested the speaker to give his/her open problems there.
Many interesting problems were presented in these problem sessions and, based on them, we had valuable discussions in and between seminars and the workshop.
I edited open problems discussed there into a problem list, which, I hope, will clarify the present frontier of this area and assist readers when considering future directions.
The proceedings of the workshop was published in the online journal "Geometry and Topology Monographs".
The problem list will also be published as a part of the proceedings.
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