| Project/Area Number |
13440018
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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 |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
MURAKAMI Hitoshi 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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| Co-Investigator(Kenkyū-buntansha) |
SAITO Kyouji Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20012445)
KOBAYASHI Tsuyoshi Nara Women's University Department of Mathematics, Faculty of Science, Professor, 理学部, 教授 (00186751)
OOTSUKI Tomotada Kyoto University, Research Institute for Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (50223871)
MURAKAMI Jun Waseda University, Department of Mathematical Sciences, School of Science and Engineering, Professor, 理工学部, 教授 (90157751)
TANIYAMA Kouki Waseda University, Department of Science, School of Education, Associate Professor, 教育学部, 助教授 (10247207)
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| Project Period (FY) |
2001 – 2002
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| Keywords | knot / 3-manifold / quantum ivariant / lowdimensional topology / graph |
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| Research Abstract |
The academic year 2001: We organized the yearlong Research Project 'Low-Dimensional Topology in the 21st Century' at the Research Institute for Mathematical Sciences, Kyoto University
In this project we invited low-dimensional topologists from inside and outside Japan. We had about 50 visitors from overseas and we could exchange information and could discuss on various areas with many lectures. Consequently we could obtain new aspects on many areas in low-dimensional topology such as combinatorial study of three-dimensional manifolds, knotted surfaces in four-dimensional manifolds, and quantum invariants of knots and three-manifolds.
The academic year 2002 : We publicized our results obtained in the academic year 2001. We also exchanged ideas with researchers and thus could make our new goals.
In April the head investigator and Jun Murakami were invited to a workshop on the volume conjecture held at the University of Quebec at Montreal, Canada and gave talks. The volume conjecture was proposed by Jun Murakami and the head investigator generalizing R. Kashaev's conjecture. It would relate the colored Jones polynomials of knots to the geometric structures of the knot complements, and attracts many researchers all over the world. Kobayashi visited Korea Advanced Institute for Science and Technology in July and gave a series of lectures on three-dimensional manifolds. Taniyama gave an invited lecture on links in graphs at the international conference 'Geometric Topology' held at Xian, China. Ohtsuki published a book 'Quantum invariants ・・A study of knots, 3-manifolds, and their sets', which describes quantum invariants including his own results.
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