Abstract
This is a résumé of the author's recent work on certain analogies between primes and links. The purpose of this article is to introduce a new invariant, called Milnor invariant, in algebraic number theory, based on an analogy between the structure of a certain Galois group over the rational number field and that of the group of a link in three dimensional Euclidean space. It then turns out that the Legendre, Rédei symbols are interpreted as our link invariants. We expect that this is a tip of an arithmetical theory after the model of link theory which may give a new insight in algebraic number theory. The details will be published elsewhere.
| Original language | English |
|---|---|
| Pages (from-to) | 18-21 |
| Number of pages | 4 |
| Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |
| Volume | 76 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jan 1 2000 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
Milnor's link invariants attached to certain Galois groups over Q. / Morishita, Masanori.
In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 76, No. 2, 01.01.2000, p. 18-21.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Milnor's link invariants attached to certain Galois groups over Q
AU - Morishita, Masanori
PY - 2000/1/1
Y1 - 2000/1/1
N2 - This is a résumé of the author's recent work on certain analogies between primes and links. The purpose of this article is to introduce a new invariant, called Milnor invariant, in algebraic number theory, based on an analogy between the structure of a certain Galois group over the rational number field and that of the group of a link in three dimensional Euclidean space. It then turns out that the Legendre, Rédei symbols are interpreted as our link invariants. We expect that this is a tip of an arithmetical theory after the model of link theory which may give a new insight in algebraic number theory. The details will be published elsewhere.
AB - This is a résumé of the author's recent work on certain analogies between primes and links. The purpose of this article is to introduce a new invariant, called Milnor invariant, in algebraic number theory, based on an analogy between the structure of a certain Galois group over the rational number field and that of the group of a link in three dimensional Euclidean space. It then turns out that the Legendre, Rédei symbols are interpreted as our link invariants. We expect that this is a tip of an arithmetical theory after the model of link theory which may give a new insight in algebraic number theory. The details will be published elsewhere.
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UR - http://www.scopus.com/inward/citedby.url?scp=23044519290&partnerID=8YFLogxK
U2 - 10.3792/pjaa.76.18
DO - 10.3792/pjaa.76.18
M3 - Article
AN - SCOPUS:23044519290
VL - 76
SP - 18
EP - 21
JO - Proceedings of the Japan Academy Series A: Mathematical Sciences
JF - Proceedings of the Japan Academy Series A: Mathematical Sciences
SN - 0386-2194
IS - 2
ER -