1988 Fiscal Year Final Research Report Summary
| Project/Area Number |
62302001
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
MATUMOTO Takao Hiroshima University, Faculty of Science, Associate Professor, 理学部, 助教授 (50025467)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIKAWA Seiki Kyushu University, Faculty of Science, Associate Professor, 理学部, 助教授 (60004488)
UENO Kenji Kyoto University, Faculty of Science, Professor, 理学部, 教授 (40011655)
MORITA Shigeyuki Tokyo Institute of Technology, faculty of Science, Professor, 理学部, 教授 (70011674)
MATSUMOTO Yukio University of Tokyo, Faculty of Science, Associate Professor, 理学部, 助教授 (20011637)
KAWAUCHI Akio Osaka City University, Faculty of Science, Professor, 理学部, 教授 (00112524)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Geometry of manifolds / Topology of manifolds / 3-dimensional manifolds / 4-dimensional manifolds / Geometry of the modulispace / Knot theory / Casson's invariant / 数学と場の理論 |
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| Research Abstract |
The research of 2,3 and 4-dimensional manifolds in now related to the geometry of manifolds including the moduli spaces and also to the physics especially the theory of field. The link polynomials are investigated at the knot theory meeting through Yang-Baxter equations, completely solvable models, representations of Hecke algebras and IRF models. A report in a book from is published in Japanese. the imitation theory which assures the existence of the hyperbolic manifolds having the same homology with a given 3-dimensional manifold even after taking any covering is completed and now seeks applications(Kawauchi). The topology of 3dimensional homology spheres are studied by the moduli space of instantons and the mapping class group(Morita) and Milnor fiberings (Matsumoto). The metric structures on the moduli space of instantons are also studied(Matumoto). Conformal field theory over the ring of integers is investigated(Ueno) and another mathematically rigorous conformal field theory is formulated(Tsuchiya). The spectral invariants of the riemannian foliations are studied by using the fundamental solutions of a degenerated heat equation(Nishikawa). The cooperation of mathematicans and physicists becomes familiar and a report written mostly in Japanese of such a meeting on the topological aspects of modern physics is avaiable.
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