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Hurwitz action on systems of braids

Research Project

Project/Area Number 23840026
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionGunma National College of Technology (2012)
Hiroshima University (2011)

Principal Investigator

YAGUCHI Yoshiro  群馬工業高等専門学校, 一般教科(自然科学), 講師 (90613018)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsブレイド群 / Hurwitz作用 / ブレイド状曲面 / コード / 曲面ブレイド / 曲面絡み目
Research Abstract

1) Hurwitz equivalence on systems of braids is studied, which can be used in the study of braided surfaces. We obtained some invariants of the Hurwitz equivalence on the systems of braids by using the first Johnson homomorphism of the braid group. Then, we found some invariants of braided surfaces.2) A cord is a simple curve on a punctured disk, which connects two punctures. We introduced diagrams which represent isotopy classes of cords. Using such diagrams, we made up a list of all isotopy classes of cords on a 3-times punctured disk. As a result, it was shown that they are completely parameterized by 3 non-negative integers.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • Research Products

    (33 results)

All 2013 2012 2011 Other

All Presentation (30 results) (of which Invited: 2 results) Remarks (3 results)

  • [Presentation] Hurwitz action の紹介と単純2次元ブレイドの不変量2013

    • Author(s)
      矢口義朗
    • Place of Presentation
      群馬大学,Hurwitz action とその周辺
    • Related Report
      2012 Final Research Report
  • [Presentation] Hurwitz action の紹介と単純2次元ブレイドの不変量2013

    • Author(s)
      矢口義朗
    • Organizer
      Hurwitz actionとその周辺
    • Place of Presentation
      群馬大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Homological invariants of Hurwitz action on tuples of simple braids2012

    • Author(s)
      矢口義朗
    • Organizer
      AMS Sectional Meeting AMS Special Session
    • Place of Presentation
      米国(招待講演)
    • Year and Date
      2012-03-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hurwitz actionについての紹介,およびブレイド群の直積へのHurwitz actionとその応用2012

    • Author(s)
      矢口義朗
    • Organizer
      研究集会「Hurwitz action」
    • Place of Presentation
      大阪市(招待講演)
    • Year and Date
      2012-01-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Homological invariants of Hurwitz equivalence on tuples of simple braids2012

    • Author(s)
      矢口義朗
    • Organizer
      The 8th East Asian School of Knots and Related Topics
    • Place of Presentation
      韓国(招待講演)
    • Year and Date
      2012-01-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Homological invari- ants of Hurwitz equivalence on tuples of simple braids2012

    • Author(s)
      Yoshiro Yaguchi
    • Organizer
      The 6th East Asian School of Knots and Related Topics
    • Place of Presentation
      KAIST
    • Related Report
      2012 Final Research Report
  • [Presentation] On the extended 1-st Johnsonhomomorphism of the braid group2012

    • Author(s)
      矢口義朗
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学
    • Related Report
      2012 Final Research Report
  • [Presentation] ブレイド群の第1ジョンソン準同型について2012

    • Author(s)
      矢口義朗
    • Organizer
      神戸トポロジーセミナー
    • Place of Presentation
      神戸大学
    • Related Report
      2012 Final Research Report
  • [Presentation] ブレイド群のジョンソン準同形の計算方法について2012

    • Author(s)
      矢口義朗
    • Organizer
      てんぶす那覇
    • Place of Presentation
      琉球結び目セミナー
    • Related Report
      2012 Final Research Report
  • [Presentation] On simple paths in apunctured disk and their applicationsto simple braids2012

    • Author(s)
      矢 口 義朗
    • Organizer
      4次元ト ポロジー
    • Place of Presentation
      広島大学
    • Related Report
      2012 Final Research Report
  • [Presentation] 穴あき円板内の単純曲線のリ ストと2次元ブレイド不変量への応用2012

    • Author(s)
      矢口義朗
    • Place of Presentation
      学習院大学学習院トポロジーセミナー
    • Related Report
      2012 Final Research Report
  • [Presentation] On the extended 1-st Johnson homomorphism of the braid group2012

    • Author(s)
      矢口義朗
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] ブレイド群の第1ジョンソン準同型について2012

    • Author(s)
      矢口義朗
    • Organizer
      神戸トポロジーセミナー
    • Place of Presentation
      神戸大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] ブレイド群のジョンソン準同形の計算方法について2012

    • Author(s)
      矢口義朗
    • Organizer
      2012琉球結び目セミナー
    • Place of Presentation
      てんぶす那覇
    • Related Report
      2012 Annual Research Report
  • [Presentation] On simple paths in a punctured disk and their applications to simple braids2012

    • Author(s)
      矢口義朗
    • Organizer
      4次元トポロジー
    • Place of Presentation
      広島大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 穴あき円板内の単純曲線のリストと2次元ブレイド不変量への応用2012

    • Author(s)
      矢口義朗
    • Organizer
      学習院トポロジーセミナー
    • Place of Presentation
      学習院大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Homological invariants of Hurwitz equivalence on braid monodromies2011

    • Author(s)
      矢口義朗
    • Organizer
      阪大トポロジーセミナー
    • Place of Presentation
      大阪市(招待講演)
    • Year and Date
      2011-12-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Homological invariants of Hurwitz equivalence on systems of simple braids2011

    • Author(s)
      矢口義朗
    • Organizer
      離散群と双曲空間の解析と幾何
    • Place of Presentation
      京都市(招待講演)
    • Year and Date
      2011-12-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hurwitz equivalence on simple braid systems2011

    • Author(s)
      矢口義朗
    • Organizer
      Four Dimensional Topology
    • Place of Presentation
      東広島市
    • Year and Date
      2011-11-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Homological invariants of systems of simple braids2011

    • Author(s)
      矢口義朗
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市(招待講演)
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] 曲面ブレイドの分類へ向けて2011

    • Author(s)
      矢口義朗
    • Organizer
      研究集会「リーマン面に関連する位相幾何学」
    • Place of Presentation
      東京都文京区(招待講演)
    • Year and Date
      2011-09-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hurwitz action on tuples of simple braids2011

    • Author(s)
      矢口義朗
    • Organizer
      第3回KOOK-TAPU合同Seminar
    • Place of Presentation
      大阪市(招待講演)
    • Year and Date
      2011-07-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hurwitz action on tuples of simple braids2011

    • Author(s)
      Yoshiro Yaguchi
    • Organizer
      第3回KOOK-TAPU合同Seminar
    • Place of Presentation
      大阪市立大学
    • Related Report
      2012 Final Research Report
  • [Presentation] 曲面ブレイドの分類に向けて2011

    • Author(s)
      矢口義朗
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Homological invariants of systems of simple braids2011

    • Author(s)
      矢口義朗
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大 学
    • Related Report
      2012 Final Research Report
  • [Presentation] Hurwitz equivalence on simple braid systems2011

    • Author(s)
      矢 口 義 朗
    • Organizer
      4次 元トポロジー
    • Place of Presentation
      広島大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Homological invariants of Hurwitz equivalence on systems of simple braids2011

    • Author(s)
      矢口義朗
    • Organizer
      離散群と双曲 空間の解析と幾何
    • Place of Presentation
      京都大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Homological invariants of Hurwitz equivalence on braid mono- dromies2011

    • Author(s)
      矢口義朗
    • Organizer
      阪大トポロジーセミ ナー
    • Place of Presentation
      大阪大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Hurwitz action についての紹 介,およびブレイド群の直積への Hurwitz action と その 応 用2011

    • Author(s)
      矢口義朗
    • Organizer
      Hurwitz action
    • Place of Presentation
      大阪市立大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Homological invari- ants of Hurwitz action on tuples of simple braids2011

    • Author(s)
      Yoshiro Yaguchi
    • Organizer
      AMS
    • Place of Presentation
      南フロリダ大学
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://yyaguchi.web.fc2.com/

    • Related Report
      2012 Final Research Report
  • [Remarks] 矢口義朗のホームページ

    • URL

      http://yyaguchi.web.fc2.com/

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://yyaguchi.web.fc2.com/

    • Related Report
      2011 Annual Research Report

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Published: 2011-09-05   Modified: 2019-07-29  

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