Analogies between primes and knots, number theory and 3-dim. Topology

点击翻译按钮获取中文摘要

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.