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

基于质数和结之间的类比，我研究了数论3-dim之间的联系。拓扑。我写了5篇论文和2篇调查日语的文章。论节与质数之间的某些类比，Crelle J. 550, 2002。基于链群和伽罗瓦群之间的类比，我讨论了结点和素数之间的类比（Alexander ino* luks， Milnor * nvariiceuts for素数）。链接环复盖的属理论，日本。2001年第77期。我对环的循环复盖给出了热理论的类比。关于3-流形的大写问题。伽罗瓦理论与模量理论，2003。我给出了3-流形覆盖的大写定理的拓扑类比。米尔诺：素数的不变量和梅西积，《合成数学》。2004年出现。从伽罗瓦上同的梅西积的角度给出了素数的米尔诺不变量的解释。质数和结（日语）。代数研讨会进程。2002.6. 数论和3-dim。拓扑(日本)。Surikagaku, 2003年。July.7。结与素数、3流形与数域之间的类比，（已提交）这是算术拓扑的基础调查文章，讨论了结与素数、3流形与数域之间的类比。我曾在几次国际会议上就这些作品发表过演讲。

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.