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The existences of epimorphisms between knot groups and their geometric interpretations

Research Project

Project/Area Number 16K05159
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Suzuki Masaaki  明治大学, 総合数理学部, 専任教授 (70431616)

Project Period (FY) 2016-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords結び目群 / 全射準同型 / 全射凖同型 / 低次元トポロジー
Outline of Final Research Achievements

A knot is an embedded circle. The knot group of a knot is a fundamental group of the exterior of a knot. The fundamental group is the set of loops where two loops are considered as the same element if they are transformed continuously. The knot group characterizes a knot. However, it is very complicated. Then in this research, we considered whether there exists an epimorphism between knot groups and their geometric interpretations.

Academic Significance and Societal Importance of the Research Achievements

結び目群は結び目をとてもよく特徴づけているが、一般に群を調べることは容易ではないことが多い。そのため、その間の全射準同型の存在という関係を調べることは意味がある。このようにそのものが単独では複雑で扱いにくいものでも、それらの関係を調べるということで研究を進めるという方法は様々な場面で応用できるものと考えられ、その点でも意義があると考える。

Report

(8 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (39 results)

All 2022 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (5 results) Journal Article (15 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 15 results,  Acknowledgement Compliant: 2 results) Presentation (19 results) (of which Int'l Joint Research: 10 results,  Invited: 12 results)

  • [Int'l Joint Research] The University of Texas at Dallas(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] University of Texas at Dallas(米国)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] POSTECH(韓国)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] University of Texas at Dallas(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] POSTECH(韓国)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor2022

    • Author(s)
      Y. Nozaki, M. Sato, and M. Suzuki
    • Journal Title

      Geometry and Topology

      Volume: 26 Pages: 221-282

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the kernel of the surgery map restricted to the 1-loop part2022

    • Author(s)
      Y. Nozaki, M. Sato, and M. Suzuki
    • Journal Title

      Journal of Topology

      Volume: 15 Pages: 587-619

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a theorem of Friedl and Vidussi2022

    • Author(s)
      T. Morifuji and M. Suzuki
    • Journal Title

      International Journal of Mathematics

      Volume: 33 Pages: 14-14

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions on epimorphisms between $2$-bridge knot groups2021

    • Author(s)
      Masaaki Suzuki
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 30 Pages: 24-24

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Torelli group, Johnson kernel and invariants of homology spheres2020

    • Author(s)
      S. Morita, T. Sakasai, M. Suzuki
    • Journal Title

      Quantum Topology

      Volume: 11 Pages: 379-410

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Alternating knots with Alexander polynomials having unexpected zeros2019

    • Author(s)
      M. Hirasawa, K. Ishikawa, M. Suzuki
    • Journal Title

      Topology and its Applications

      Volume: 253 Pages: 48-56

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Genera of two-bridge knots and epimorphisms of their knot groups2018

    • Author(s)
      Anh, Tran and Masaaki Suzuki
    • Journal Title

      Topology and its Applications

      Volume: 242 Pages: 66-72

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra2018

    • Author(s)
      Shigeyuki Morita, Takuya Sakasai, and Masaaki Suzuki
    • Journal Title

      Experimental Mathematics

      Volume: 27 Pages: 302-315

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Symmetry of symplectic derivation Lie algebra of free Lie algebras2017

    • Author(s)
      S. Morita, T. Sakasai, and M. Suzuki
    • Journal Title

      RIMS Kokyuroku Bessatsu, Geometry and Analysis of Discrete Groups and Hyperbolic Spaces

      Volume: B66 Pages: 185-194

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Epimorphisms between 2-bridge knot groups and their crossing numbers2017

    • Author(s)
      Masaaki Suzuki
    • Journal Title

      Algebraic and Geometric Topology

      Volume: 17 Pages: 2413-2428

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra2017

    • Author(s)
      Shigeyuki Morta, Takuya Sakasai, and Masaaki Suzuki
    • Journal Title

      Experimental Mathematics

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Symmetry of symplectic derivation Lie algebras of free Lie algebras2017

    • Author(s)
      Shigeyuki Morta, Takuya Sakasai, and Masaaki Suzuki
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] On minimality of two-bridge knots2017

    • Author(s)
      Fumikazu Nagasato, Masaaki Suzuki, and Anh Tran
    • Journal Title

      International Journal of Mathematics

      Volume: 28

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Epimorphisms between $2$-bridge knot groups and their crossing numbers2017

    • Author(s)
      Masaaki Suzuki
    • Journal Title

      Algebraic and Geometric Topology

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Monodromy maps of fibered $2$-bridge knots as elements in Automorphism of free groups2016

    • Author(s)
      Hiroshi Goda and Masaaki Suzuki
    • Journal Title

      Kyungpook Mathematical Journal

      Volume: 56 Pages: 927-938

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] On a theorem of Friedl and Vidussi2022

    • Author(s)
      鈴木正明
    • Organizer
      トポロジーとコンピュータ
    • Related Report
      2022 Annual Research Report
  • [Presentation] Genera and crossing numbers of 2-bridge knots2022

    • Author(s)
      鈴木正明
    • Organizer
      日本数学会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Genera and crossing numbers of 2-bridge knots2022

    • Author(s)
      鈴木正明
    • Organizer
      拡大KOOKセミナー
    • Related Report
      2022 Annual Research Report
  • [Presentation] Knot group, symmetric group, dihedral group, and twisted Alexander polynomial2022

    • Author(s)
      Masaaki Suzuki
    • Organizer
      East Asian Conference on Geometric Topology
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Epimorphisms between knot groups and twisted Alexander polynomial2022

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology and Geometry of Low-dimensional Manifolds
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Generating function on epimorphisms between 2-bridge knot groups2021

    • Author(s)
      Masaaki Suzuki
    • Organizer
      East Asian Conference on Geometric Topology 2021
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Epimorphisms between two-bridge knot groups - crossing number, genus2020

    • Author(s)
      Masaaki Suzuki
    • Organizer
      トポロジーとコンピュータ2020
    • Related Report
      2020 Research-status Report
  • [Presentation] On a structure of the symplectic derivation Lie algebra of the free Lie algebra2020

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Teichmuller Theory: Classical, Higher, Super and Quantum
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Epimorphisms between knot groups2020

    • Author(s)
      Masaaki Suzuki
    • Organizer
      SFB Seminar
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Two filtrations of the Torelli group2019

    • Author(s)
      Masaaki Suzuki
    • Organizer
      East Asian Conference on Geometric Topology 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Computations of Johnson homomorphisms2018

    • Author(s)
      Masaaki Suzuki
    • Organizer
      New Trends in Teichmuler Theory and Mapping Class Groups
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Genera of two-bridge knots and epimorphisms of their knot groups2018

    • Author(s)
      Masaaki Suzuki
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
  • [Presentation] Genera of two-bridge knots and epimorphisms of their knot groups2018

    • Author(s)
      Masaaki Suzuki
    • Organizer
      東北結び目セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Two filtrations of the Torelli group2018

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology and Computer 2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Epimorphisms between knot groups2017

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Seminar Geometry, Topology, Dynamical Systems
    • Place of Presentation
      University of Texas at Dallas
    • Year and Date
      2017-03-21
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Epimorphisms between knot groups - crossing number, genus2017

    • Author(s)
      Masaaki Suzuki
    • Organizer
      East Asian School of Knots and Related Topics
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Epimorphisms between two-bridge knot groups and their crossing numbers2016

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Fundamental Groups, Representations and Geometric Structures in 3-Manifold Topology
    • Place of Presentation
      Hiroshima University
    • Year and Date
      2016-11-22
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Epimorphisms between knot groups2016

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Geometry Seminar
    • Place of Presentation
      University of Pau
    • Year and Date
      2016-11-15
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Epimorphisms between knot groups2016

    • Author(s)
      Masaaki Suzuki
    • Organizer
      International Conference for the 70th Anniversary of Korean Mathematical Society
    • Place of Presentation
      Seoul National University
    • Year and Date
      2016-10-22
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2016-04-21   Modified: 2024-01-30  

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