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Geometry of the braid groups and mapping class groups and their growth

Research Project

Project/Area Number 18K03283
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11020:Geometry-related
Research InstitutionUniversity of the Ryukyus

Principal Investigator

Fujii Michihiko  琉球大学, 理学部, 教授 (60254231)

Co-Investigator(Kenkyū-buntansha) 河澄 響矢  東京大学, 大学院数理科学研究科, 教授 (30214646)
逆井 卓也  東京大学, 大学院数理科学研究科, 准教授 (60451902)
佐藤 隆夫  東京理科大学, 理学部第二部数学科, 教授 (70533256)
Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords離散群 / 増大級数 / ブレイド群 / ザイフェルト・ファイバー空間 / ケーリー・グラフ / 基本群 / 測地的代表元 / ガ―サイド標準形 / スータブル・スプレッド法 / 随伴群 / ケーリーグラフ / ザイフェルトファイバー空間 / ガーサイド標準形 / 写像類群 / 増大度
Outline of Final Research Achievements

The principal investigator Fujii and the co-investigators succeeded in constructing algorithms to compute the spherical growth series for the adjoint groups with respect to the braid groups in simple cases and the fundamental groups of certain Seifert fibered spaces.

Academic Significance and Societal Importance of the Research Achievements

離散群の増大級数は、幾何学的群論において重要な研究テーマであるにもかかわらず、個々の離散群に対して、具体的に増大級数を求めることは一般に難しい。本研究では、幾何において重要な離散群の増大級数をいくつか具体的に求めることに成功した。この計算結果および計算過程で用いられた手法を分析することによって、3次元多様体の基本群やブレイド群などに関連して、数理物理、表現論、暗号理論などの他分野への応用をもたらすことが期待できる。

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (5 results)

All 2024 2023 2021 2018

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results)

  • [Journal Article] A new formula for the spherical growth series of an amalgamated free product of two infinite cyclic groups2018

    • Author(s)
      Michihiko Fujii
    • Journal Title

      Kodai Mathematical Journal

      Volume: 41 Pages: 475-511

    • NAID

      130007506557

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] Growth of Garside Groups2024

    • Author(s)
      藤井道彦
    • Organizer
      拡大版「リーマン面・不連続群論」
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] The spherical growth series of amalgamated free products of infinite cyclic groups2023

    • Author(s)
      藤井道彦、逆井卓也
    • Organizer
      日本数学会・秋季総合分科会
    • Related Report
      2023 Annual Research Report
  • [Presentation] The geodesic growth of a Seifert fiber space2021

    • Author(s)
      Michihiko Fujii
    • Organizer
      RIMS Workshop, Geometry of discrete groups and hyperbolic spaces
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] How a geodesic representative of an element of the braid group is obtained2018

    • Author(s)
      藤井 道彦
    • Organizer
      Geomety of Riemann surfaces and related topics
    • Related Report
      2018 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2025-01-30  

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