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Pro-finite completion of a 3-manifold group and its relation to topological invariants

Research Project

Project/Area Number 25400101
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionSoka University

Principal Investigator

Kitano Teruaki  創価大学, 理工学部, 教授 (90272658)

Co-Investigator(Renkei-kenkyūsha) MORIFUJI Takayuki  慶応義塾大学, 経済学部, 教授 (90334466)
Research Collaborator TRAN Anh  University of Texas at Dallas
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords基本群 / Reidemeister torsion / linear representation / fundamental group / SL(2;C)-representation / minimal polynomial / Brieskorm manifold / homology sphere / homology 3-sphere / torus knot / figure-eight knot / Reidemeister torison / Dehn surgery / Brieskorn manifold / Chebychev polynomial / 結び目 / トーラス結び目 / 副有限完備化 / 自由積
Outline of Final Research Achievements

We studied 3-dimensional topology from the view point of the pro-finite completion of the fundamental group of a 3-manifold manifold. In particular we studied Reiemeister torsion for SL(2;C)-representations, which is defined by using linear representations of the fundamental group.Denis Johnson proposed some theory related with Reidemeister torsion. We obtained some formula of Reidemeister torsion, which would be related with Galois group, or Galois extensions of a field.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (14 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (9 results) (of which Invited: 1 results) Remarks (1 results)

  • [Int'l Joint Research] テキサス大学ダラス校(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Aix-Marseille University/Joseph Fourier University(France)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Introduction to twisted Alexander polynomials and related topics2016

    • Author(s)
      Teruaki Kitano
    • Journal Title

      Winter Braids Lecture Notes

      Volume: 2 Pages: 1-35

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Reidemeister torsion of a 3-manifold obtained by an integral Dehn-surgery along the figure-eight knot2016

    • Author(s)
      Teruaki Kitano
    • Journal Title

      Kodai Mathematical Journal

      Volume: 39 Pages: 290-296

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Brieskornホモロジー3 球面の基本群のSL(2;C)- 表現のReidemeister torsionから定まる多項式について2017

    • Author(s)
      北野晃朗, Anh Tran
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-25
    • Related Report
      2016 Annual Research Report
  • [Presentation] A polynomial invariant of a homology 3-sphere defined by Reidemeister torsion2017

    • Author(s)
      北野晃朗
    • Organizer
      RIMS研究集会「Casson不変量に関わる3次元多様体の不変量」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2017-01-26
    • Related Report
      2016 Annual Research Report
  • [Presentation] SL(2;R)-representations of a Brieskorn homology 3-sphere2016

    • Author(s)
      北野晃朗, 山口祥司
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] 結び目群の SL(2; C)-表現から定まる C^2 -係数ねじれ 1 次元コホモロジーとtwisted Alexander polynomial2015

    • Author(s)
      北野晃朗
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] 8の字結び目をDehn手術して得られるホモロジー球面のSL (2;C)-既約表現応するReidemeister torsionについて2015

    • Author(s)
      北野晃朗
    • Organizer
      日本数学会年会トポロジー分科会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Twisted Alexander polynomial2015

    • Author(s)
      Teruaki Kitano
    • Organizer
      Winter Braids V
    • Place of Presentation
      University of Pau
    • Year and Date
      2015-02-17 – 2015-02-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Reidemeister torsion of a homology 3-sphere obtained by 1/n-surgery along a (p,q)-torus-knot2015

    • Author(s)
      Teruaki Kitano
    • Organizer
      The tenth East Asian school of knots and related topics
    • Place of Presentation
      East China Normal University
    • Year and Date
      2015-01-28
    • Related Report
      2014 Research-status Report
  • [Presentation] トーラス結び目をDehn手術して得られるホモロジー球面のSL (2;C)-既約表現に対応するReidemeister torsionについて2014

    • Author(s)
      北野晃朗
    • Organizer
      日本数学会秋季総合分科会トポロジー分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Reidemeister torsion of a homology 3-sphere surgeried along a (p,q)-torus knot for SL(2;C)-representations2014

    • Author(s)
      Teruaki Kitano
    • Organizer
      Seoul International Congress of Mathematicians 2014
    • Place of Presentation
      Coex, Seoul, Korea
    • Year and Date
      2014-08-14
    • Related Report
      2014 Research-status Report
  • [Remarks] 研究集会「低次元多様体の基本群とその表現に関する様々な構造について」

    • URL

      http://www.t.soka.ac.jp/~kitano/Nara_wks_2013.htm

    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2022-02-16  

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