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

素数和结、数论和三维之间的类比。

基本信息

批准号：
13640014
负责人：
MORISHITA M
金额：
$ 2.24万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640014/
关键词：
prime knot number field 3-manifold Galois group link group 基本群

项目摘要

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.

基于素数与纽结的类比，研究了数论三维拓扑与素数的关系。我写了5篇论文和2篇调查日语的文章。基于环群与某个伽罗瓦群之间的类比，讨论了纽结与素数之间的某些类比（亚历山大ino**luks，Milnor *nvariceuts for primes）2.环的循环覆盖的一个理论。Acad. 77，2001.我给了一个类比的理论gevera循环覆盖的链接。3.关于3-流形的首字母大写问题，Proc.“Galois theory & Modula Forses”2003.我给出了3-流形覆盖的首字母大写定理的一个拓扑类比.米尔诺：素数的Milnor不变量和Massey积，Compositio Math.发表于2004.我给出了素数的Milnor不变量在Galois余同调的Massey积的一个定理中的解释. Primes and Knots（日语）代数研讨会论文集。2002.6.数论与三维拓扑（日文）。Surikagaku，2003年。七月七日。纽结和素数之间的类比，3-流形和数域，（已提交）这些是算术拓扑讨论纽结和素数之间的类比，3-流形和数域的基础调查文章。我在几个国际会议上就这些作品发表了演讲。