2002 Fiscal Year Final Research Report Summary
Analogies between primes and knots, number theory and 3-dim. Topology
| Project/Area Number |
13640014
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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 | Kanazawa University |
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Principal Investigator |
MORISHITA M Kanazawa Univ. Math. Dept. Ass. Prof., 理学部, 助教授 (40242515)
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| Co-Investigator(Kenkyū-buntansha) |
HAYAKAWA T Kanazawa Univ. Math. Dept. Ass., 理学部, 助手 (20198823)
SUGANO T Kanazawa Univ. Math. Dept. Prof., 理学部, 教授 (30183841)
YAMAGISHI M Nagoya Inst. Of Tech. Asso. Prof., 工学部, 助教授 (40270996)
岩瀬 順一 金沢大学, 理学部, 助手 (70183746)
IWASE J Kanazawa Univ. Math. Dept. Ass., 理学部, 助手 (50293337)
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| Project Period (FY) |
2001 – 2002
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| Keywords | prime / knot / number field / 3-manifold / Galois group / link group |
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| Research Abstract |
Base on the analogies between primes and knots, I studied the connection between number theory 3-dim. Topology. I wrote 5 papers and 2 survey Japanese articles.
1. On certain analogies between knots and primes, Crelle J. 550, 2002.
Based on the analogy between a link group and a certain Galois group, I discussed some analogies between knots and primes (Alexander ino**luks, Milnor *nvariceuts for primes)
2. A theory of genera for cyclic coverings of links, Proc. Japan. Acad. 77, 2001.
I gave an analogy of the theory of gevera for cyclic coverings of links.
3. On capitalation problem for 3-manifolds, Proc. "Galois theory & Modula Forses" 2003.
I gave a topological analog of the capitalation theorems for coverings of 3-manifolds.
4. Milnor : invariants and Massey products for prime numbers, Compositio Math. To appear 2004.
I gave an interpretation of Milnor invariouts for primes in teerms of the Massey products of Galois cohomology.
5. Primes and Knots (Japanese). Proc. Of algebra symposium. 2002.
6. Number theory and 3-dim. Topology (Japanese). Surikagaku, 2003. July.
7. Analogies between Knots and primes, 3-manifolds and number fields, (Submitted)
These are foundational survey articles on arithmetic topology discussing anelogies between knots and primes, 3-manifolds and number fields.
I gave talks on these works at several international conferences.
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