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2004 Fiscal Year Final Research Report Summary

Study of analogies between algebraic number theory and 3-dimensional topology.

Research Project

Project/Area Number 15540017
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKanazawa University

Principal Investigator

MORISHITA Masanori  Kanazawa Univ., Dept.of Math., Associate Prof., 大学院・自然科学研究科, 助教授 (40242515)

Co-Investigator(Kenkyū-buntansha) KURIHARA Masato  Tokyo Metro., Dept.of Math., Associate Prof., 理学部, 助教授 (40211221)
TAGUCHI Yuichiro  Kyushu Univ., Dept.of Math., Associate Prof., 大学院・数理学研究院, 助教授 (90231399)
KOHNO Toshitake  Tokyo Univ., Dept.of Math.Sci., Prof., 大学院・数理科学研究科, 教授 (80144111)
SUGANO Takashi  Kanazawa Univ., Dept.of Math., Prof., 自然科学研究科, 教授 (30183841)
野村 明人  金沢大学, 自然科学研究科, 助教授 (00313700)
USHIJIMA Akira  Kanazawa Univ., Dept.of Math., Lect. (50323803)
Project Period (FY) 2003 – 2004
Keywordsprime / knot / number field / 3-manifold
Research Abstract

I have worked on analogies between algebraic number theory and 3-dimensuonal topology, based on the analogy between primes and Knots. More precise results I obtained are as fellows.
1)I have pursued analogies between Iwasawa theory and Alexandev-Fox theory. In particular, I found that the relation between topological and analytical fusions is regarded as an analogue of the Iwasawa main Conjecture. giving the relation between algebraic Iwasawa polynomial and analytic p-adie L-functions. I have a research plan to pursue analogies in the context of geometry of Kato's Theory of zeta elements, the formulation of generalized Iwasawa main conjecture etc.
2)I have pursued analogies between the spaces of deformations of Galore representations and the character varieties of a knot group and found a certain analogy between the space of Hida's deformations and the She character variety of a hyperbolic knot group. I have a research plan to pursue analogies of 2-dimensional p-adie L-functions in the context of P of theory.

  • Research Products

    (6 results)

All 2005 2004

All Journal Article (6 results)

  • [Journal Article] 幾何学と数論2005

    • Author(s)
      森下昌紀
    • Journal Title

      数理科学 506(未定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Geometry and Number Theory2005

    • Author(s)
      M.Morishita
    • Journal Title

      Surikagaku (Science-Sya) (To appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Milnor ihvariants and l-class groups2005

    • Author(s)
      M.Morishita
    • Journal Title

      (Submitted)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On analogies between primes and knots2005

    • Author(s)
      M.Morishita
    • Journal Title

      (Submitted)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] 素数と結び目2004

    • Author(s)
      森下昌紀
    • Journal Title

      数学のたのしみ(季刊) 2

      Pages: 125-144

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Primes and knots.2004

    • Author(s)
      M.Morishita
    • Journal Title

      Sugaku-no-Tanoshimi. (Nippon-Hyoron-Sha)

      Pages: 125-144

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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