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2006 Fiscal Year Final Research Report Summary

Stady of Arithmcfc Topology

Research Project

Project/Area Number 17540020
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKYUSHU UNIVERCITY

Principal Investigator

MORISHITA Masanori  Kyushu University, Faculty of Mathematics, Professor, 大学院数理学研究院, 教授 (40242515)

Co-Investigator(Kenkyū-buntansha) TAGUCHI Yushiro  Kyushu University, Faculty of Mathematics, Associate Professor, 大学院数理学研究院, 助教授 (90231399)
KANHARA Masato  Keio University, Faculty of Science, Professor, 理工学部, 教授 (40211221)
FUJII Michihiko  Kyoto University, Faculty of Science, Associate Professor, 大学院理工研究科, 助教授 (60254231)
TERASHMA Yuji  Tokyo Institute Technology, Faculty of Science, Assistant, 大学院理工学研究科, 助手 (70361764)
KOHNO Toshtake  University of Tokyo, Faculfy of Mathematical Science, 大学院数理科学研究科, 教授 (80144111)
Project Period (FY) 2005 – 2006
KeywordsKnots / Primes
Research Abstract

Based on analogies between knots and primes, I investigated the connection and interaction between knot theory and number theory. In this year, my concern has been focused on the following topics :
I showed the analogy between the structure of the deformation space of hyperbolise structures on a knot complement and the deformation space of p-adic Galvis representations of a prime group. Based on this analogy, I discussed some analogous features between the variation of Sh_2(C) Chern-Simons. in variants and p-adre modulus L-function. In particular, I gave an interpretation of the Chern-Simons invariant in terms of Deligne cohomology, Jointly with Y.Terashima. I talked about Dnr results in the international conferees hold at Hiroshima Univ.(2006,July), Max Plank Inst.(2006,Sept) and Kyoto Un.(2006,Dec)

  • Research Products

    (8 results)

All 2007 2006 Other

All Journal Article (8 results)

  • [Journal Article] Anclogies between Knots and primes, 3-manifolds and number rings2007

    • Author(s)
      M.Morishita
    • Journal Title

      Sugaku Expositions (to appear)(掲載決定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Arithmehc topology after Hide theory2007

    • Author(s)
      Morishita, Terachima
    • Journal Title

      Proc. of Intelligenu of Low. Dim. Topology (to appear)(掲載決定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the Alexander stratification in the deformation Space of Galois characters2006

    • Author(s)
      M.Morishita
    • Journal Title

      Kynshu Journal of Mathemafies 60, 2

      Pages: 405-414

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Pro-P link groups and P-homology groups2006

    • Author(s)
      Hillman, Matei Morishifa
    • Journal Title

      Contemporary Mathematics,AMS 416

      Pages: 121-136

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the Alexander stratification in the deformation space of Galois characters2006

    • Author(s)
      M.Morishita
    • Journal Title

      Kyushu Journal of Math. Vol 60

      Pages: 405-414

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Pro-p link groups and p-homology groups2006

    • Author(s)
      J.Hillman, D.Matei, M.Morishita
    • Journal Title

      Contemporary Mathematics, AMS Vol 416

      Pages: 121-136

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Analogies between knots and primes, 3-manifolds and number fields.

    • Author(s)
      M.Morishita
    • Journal Title

      Sugaku Expositions, AMS (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Arithmetic topology after Hida theory.

    • Author(s)
      M.Morishita, Y.Terashima
    • Journal Title

      Proc of Intelligence of Low Dim Topology (to appear)

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

URL: 

Published: 2008-05-27  

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