Tanaka Kokoro 田中心

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TANAKA Kokoro 田中心

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Researcher Number	70448950
Affiliation (Current)	2025: 東京学芸大学, 教育学部, 教授
Affiliation (based on the past Project Information) *help	2025: 東京学芸大学, 教育学部, 教授 2015 – 2023: 東京学芸大学, 教育学部, 准教授 2014: 東京学芸大学, 教育学部, 講師 2008 – 2011: Tokyo Gakugei University, 教育学部, 講師 2007: Gakushuin University, 理学部, 助教
Review Section/Research Field	Principal Investigator Geometry / Basic Section 11020:Geometry-related / Geometry
Keywords	Principal Investigator カンドル / 曲面結び目 / トポロジー / 低次元トポロジー / 結び目 / 位相幾何 / 結び目理論 / カンドル代数 / ミルナー不変量 / 絡み目不変量 … More / ザリスキー対 / 複素射影平面 / 平面配置 / 古典的結び目 / バイカンドル / bridge trisection表示 / bridge trisection / はめ込み / ローズマン変形 / コバノフ理論 Less

曲面結び目とカンドルコサイクル不変量Principal Investigator
- Principal Investigator
  
  田中心
- Project Period (FY)
  2025 – 2028
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Tokyo Gakugei University
カンドル代数と曲面結び目理論Principal Investigator
- Principal Investigator
  
  田中心
- Project Period (FY)
  2021 – 2024
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Tokyo Gakugei University
Elucidation of the geometric meaning of surface knot invariants defined by quandles and its applicationPrincipal Investigator
- Principal Investigator
  
  TANAKA Kokoro
- Project Period (FY)
  2017 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Gakugei University
複素射影平面上の直線配置と絡み目のミルナー不変量の研究Principal Investigator
- Principal Investigator
  
  田中心, 安原晃
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for JSPS Fellows
- Research Field
  
  Geometry
- Research Institution
  Tokyo Gakugei University
Study of Roseman moves using quandle theory and immersion theoryPrincipal Investigator
- Principal Investigator
  
  Tanaka Kokoro
- Project Period (FY)
  2014 – 2016
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Gakugei University
Elucidation of diagrammatic properties of surface-knots and construction of new invariants of surface-knotsPrincipal Investigator
- Principal Investigator
  
  TANAKA Kokoro
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Gakugei University
Research of surface-knots using quandles and Khovanov theoryPrincipal Investigator
- Principal Investigator
  
  TANAKA Kokoro
- Project Period (FY)
  2007 – 2008
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Gakugei University
  Gakushuin University

[Journal Article] Quandle colorings vs. biquandle colorings2024
- Author(s)
  Ishikawa Katsumi、Tanaka Kokoro
- Journal Title
  
  Topology and its Applications
  
  Volume: 345 Pages: 108832-108832
- DOI
  10.1016/j.topol.2024.108832
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20K14309, KAKENHI-PROJECT-21K03220
[Journal Article] The bridge number of surface links and kei colorings2022
- Author(s)
  Kouki Sato, Kokoro Tanaka
- Journal Title
  
  Bulletin of the London Mathematical Society
  
  Volume: - Issue: 5 Pages: 1763-1771
- DOI
  10.1112/blms.12654
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17K05242
[Journal Article] Shifting chain maps in quandle homology and cocycle invariants2022
- Author(s)
  Hashimoto Yu、Tanaka Kokoro
- Journal Title
  
  Transactions of the American Mathematical Society
  
  Volume: 375 Issue: 10 Pages: 7261-7276
- DOI
  10.1090/tran/8707
- Data Source
  KAKENHI-PROJECT-21K03220
[Journal Article] Homology for quandles with partial group operations2017
- Author(s)
  Scott Carter, Atsushi Ishii, Masahico Saito, Kokoro Tanaka
- Journal Title
  
  Pacific J. Math.
  
  Volume: 287-1 Issue: 1 Pages: 19-48
- DOI
  10.2140/pjm.2017.287.19
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04866, KAKENHI-PROJECT-17K05242
[Journal Article] Regular-equivalence of $2$-knot diagrams and sphere eversions2016
- Author(s)
  Masamichi Takase, Kokoro Tanaka
- Journal Title
  
  Mathematical Proceedings of the Cambridge Philosophical Society
  
  Volume: 161 (No. 2) Issue: 2 Pages: 237-246
- DOI
  10.1017/s0305004116000244
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082, KAKENHI-PROJECT-15K04880
[Journal Article] Independence of Roseman moves including triple points2016
- Author(s)
  Kengo Kawamura, Kanako Oshiro, Kokoro Tanaka
- Journal Title
  
  Algebraic & Geometric Topology
  
  Volume: 16 (No. 4) Issue: 4 Pages: 2443-2458
- DOI
  10.2140/agt.2016.16.2443
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082
[Journal Article] On rack colorings for surface-knot diagrams without branch points2015
- Author(s)
  Oshiro Kanako, Kokoro Tanaka
- Journal Title
  
  Topology and its Applications
  
  Volume: 未定
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082
[Journal Article] Charts, signatures, and stabilizations of Lefschetz fibrations2015
- Author(s)
  Hisaaki Endo, Seiichi Kamada, Isao Hasegawa, Kokoro Tanaka
- Journal Title
  
  Geometry & Topology Monographs
  
  Volume: 19
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082
[Journal Article] The shadow nature of positive and twisted quandle cocycle invariants of knots2015
- Author(s)
  Seiichi Kamada, Victoria Lebed, Kokoro Tanaka
- Journal Title
  
  Journal of Knot Theory and Its Ramifications
  
  Volume: 未定
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082
[Journal Article] A note on the local relations in geometric formalism of Khovanov homology theory2015
- Author(s)
  Kokoro Tanaka
- Journal Title
  
  Journal of Knot Theory and Its Ramifications
  
  Volume: 25 Issue: 01 Pages: 1620001-1620001
- DOI
  10.1142/s0218216516200017
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400082
[Journal Article] Complementary Regions of Knot and Link Diagrams2011
- Author(s)
  Colin Adadms, Reiko Shinjo, Kokoro Tanaka
- Journal Title
  
  Annals of Combiatorics
  
  Volume: Vol.15 Issue: 4 Pages: 549-563
- DOI
  10.1007/s00026-011-0109-2
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740042
[Journal Article] Complementary regions of knot and link diagrams2011
- Author(s)
  Colin Adams, Reiko Shinjo, Kokoro Tanaka
- Journal Title
  
  Annals of Combinatorics
  
  Volume: No.4 Pages: 549-563
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740042
[Journal Article] A note on CI-moves, Intelligence of Low Dimensional Topology 20062007
- Author(s)
  田中心
- Journal Title
  
  Ser. Knots Everything 40
  
  Pages: 307-314
- Data Source
  KAKENHI-PROJECT-19740041
[Journal Article] Inequivalent surface-knots with the same knot quandle2007
- Author(s)
  田中心
- Journal Title
  
  Topology Appl. 154 No. 15
  
  Pages: 2757-2763
- Data Source
  KAKENHI-PROJECT-19740041
[Journal Article] Inequivalent surface-knots with the same knot quandle2007
- Author(s)
  Kokoro TANAKA
- Journal Title
  
  Topology and its Applications 154
  
  Pages: 2757-2763
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19740041
[Presentation] 結び目n-カンドルのカンドル二次ホモロジー群2024
- Author(s)
  田中　心
- Organizer
  日本数学会2024年度年会「トポロジー分科会」
- Data Source
  KAKENHI-PROJECT-21K03220
[Presentation] The second quandle homology group of the knot n-quandle2024
- Author(s)
  田中　心
- Organizer
  The 19th East Asian Conference on Geometric Topology
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03220
[Presentation] The universal covering of a knot n-quandle2023
- Author(s)
  田中　心
- Organizer
  The 18th East Asian Conference on Geometric Topology
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03220
[Presentation] 二次元結び目の結び目カンドルと結び目群について2023
- Author(s)
  田中　心
- Organizer
  日本数学会2023年度年会「トポロジー分科会」
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] 結び目群は同じだが結び目カンドルは異なる球面結び目2022
- Author(s)
  田中　心
- Organizer
  ４次元トポロジー
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] カンドルから“ねじれ操作”で本質的に新しいカンドルが得られるか？2021
- Author(s)
  田中　心
- Organizer
  ハンドル体結び目とその周辺14
- Invited
- Data Source
  KAKENHI-PROJECT-21K03220
[Presentation] 結び目彩色多項式と1-タングルのカンドル彩色不変量について2021
- Author(s)
  田中　心
- Organizer
  N-KOOKセミナー
- Invited
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Knot coloring polynomial and the invariant using quandle colorings of 1-tangles2021
- Author(s)
  田中　心
- Organizer
  The 16th East Asian Conference on Geometric Topology
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Independence of Roseman moves for surface knots2020
- Author(s)
  田中心
- Organizer
  The 15th East Asian Conference on Geometric Topology
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Shifting chain maps in quandle homology and cocycle invariants2019
- Author(s)
  田中心
- Organizer
  拡大KOOKセミナー2019
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] 曲面絡み目の橋指数と圭彩色2019
- Author(s)
  田中心
- Organizer
  ４次元トポロジー
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Quandle cocycle invariants and shadow cocycle invariants2019
- Author(s)
  田中心
- Organizer
  Spring Central and Western Joint Sectional Meeting, Special Session on Algebraic and Combinatorial Structures in Knot Theory
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] 曲面結び目のbridge trisection (1)：tri-plane 図式の紹介2018
- Author(s)
  田中心
- Organizer
  2017年度琉球結び目セミナー
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Quandle 2-cocycle invariants and shadow 3-cocycle invariants2018
- Author(s)
  田中心
- Organizer
  2018年度琉球結び目セミナー
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] バイカンドル彩色数とカンドル彩色数の関係について2017
- Author(s)
  田中心
- Organizer
  東北結び目セミナー
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] A relation between biquandle colorings and quandle colorings2017
- Author(s)
  田中心
- Organizer
  研究集会「４次元トポロジー」
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Homology theory for multiple conjugation quandles2017
- Author(s)
  田中心
- Organizer
  Tsuda University Topology Workshop
- Invited
- Data Source
  KAKENHI-PROJECT-17K05242
[Presentation] Independence of Roseman moves for surface-knot diagrams2016
- Author(s)
  Kokoro Tanaka
- Organizer
  東大数理トポロジー火曜セミナー
- Place of Presentation
  東京大学数理科学研究科（東京都・目黒区）
- Invited
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] The canonical genus of Whitehead doubles of non-prime alternating knots2016
- Author(s)
  Kokoro Tanaka
- Organizer
  KOOK-TAPU Workshop of Knots in Tsushima Island
- Place of Presentation
  TIARA [下対馬離島開発センター] （長崎県・対馬市）
- Year and Date
  2016-09-06
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] バイカンドル彩色について2016
- Author(s)
  Kokoro Tanaka
- Organizer
  研究集会「2016年度琉球結び目セミナー」
- Place of Presentation
  那覇市伝統工芸館会議室（沖縄県・那覇市）
- Year and Date
  2016-12-17
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] 有向結び目図式の非同調領域数の評価について2016
- Author(s)
  Kokoro Tanaka
- Organizer
  2016 琉球結び目セミナー
- Place of Presentation
  那覇市伝統工芸館会議室(那覇市ぶんかテンブス館２階)
- Year and Date
  2016-02-20
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] Coherent regions of special diagrams of a knot2016
- Author(s)
  Kokoro Tanaka
- Organizer
  研究集会「拡大KOOKセミナー2016」
- Place of Presentation
  大阪電気通信大学（大阪府・寝屋川市）
- Year and Date
  2016-08-22
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] The canonical genus of Whitehead doubles of non-prime alternating knots2015
- Author(s)
  Kokoro Tanaka
- Organizer
  Knots in Washington XLI
- Place of Presentation
  George Washington University, Washington DC, USA
- Year and Date
  2015-12-04
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] Roseman変形の独立性について2015
- Author(s)
  Kokoro Tanaka
- Organizer
  東京女子大学トポロジーセミナー
- Place of Presentation
  東京女子大学
- Year and Date
  2015-11-28
- Invited
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] Interpretation of rack coloring knot invariants in terms of quandles2012
- Author(s)
  Kokoro Tanaka, Yuma Taniguchi
- Organizer
  The 8th East Asian School of Knots and Related Topics
- Place of Presentation
  KAIST, Daejeon(韓国)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] 曲面ブレイドのチャート表示とその局所変形について2012
- Author(s)
  田中心
- Organizer
  研究集会「Hurwitz Action」
- Place of Presentation
  大阪市立大学学術情報総合センター文化交流室(大阪府)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] Interpretation of rack coloring knot invariants in terms of quandles2012
- Author(s)
  田中心
- Organizer
  The 8th East Asian School of Knots and Related Topics
- Place of Presentation
  KAIST (Daejeon, Korea)
- Year and Date
  2012-01-10
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] Studies on surface-knots using quandle theory2010
- Author(s)
  田中心
- Organizer
  研究集会「4次元トポロジー」
- Place of Presentation
  広島大学(広島県)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] A recent approach to the smooth 4-dimensional Poincare conjectur2010
- Author(s)
  田中心
- Organizer
  Friday Seminar on Knot Theory
- Place of Presentation
  大阪市立大学数学研究所(大阪府)
- Year and Date
  2010-02-05
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] カンドル理論の曲面結び目への応用について2010
- Author(s)
  田中心
- Organizer
  第57回トポロジーシンポジウム
- Place of Presentation
  さん太ホール(岡山県)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] Khovanov homology for virtual links with two types of maps for Mobius cobordisms2010
- Author(s)
  Atsushi Ishii, Kokoro Tanaka
- Organizer
  International Conference Japan-Mexico on Topology and its Applications
- Place of Presentation
  Colima University, Colima(メキシコ)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] 曲面結び目と曲面ブレイドについて2010
- Author(s)
  田中心
- Organizer
  早稲田大学教育学部数学教室第98回7階セミナー
- Place of Presentation
  早稲田大学14号館7階717AB室(東京都)
- Year and Date
  2010-10-29
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] Rasmussen不変量とexotic 4-sphereについて:[ Freedman-Gompf-Morrison-Walker, Arxiv : GT. 0906. 5177]の紹介2009
- Author(s)
  田中心
- Organizer
  Casson-Freedman理論研究会
- Place of Presentation
  京都けいはんなプラザホテル(京都府)
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] 曲面結び目や曲面ブレイドに関するいくつかの話題2009
- Author(s)
  田中心
- Organizer
  東京女子大学トポロジーセミナー
- Place of Presentation
  東京女子大学9号館9201教室(東京都)
- Year and Date
  2009-12-05
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] カンドル理論を用いた曲面結び目の研究に関して2009
- Author(s)
  田中心
- Organizer
  信州大学トポロジーセミナー
- Place of Presentation
  信州大学理学部(長野県)
- Year and Date
  2009-11-27
- Data Source
  KAKENHI-PROJECT-21740042
[Presentation] CI変形の局所変形への分解について2008
- Author(s)
  Kokoro TANAKA
- Organizer
  日本数学会年会
- Place of Presentation
  近畿大学
- Year and Date
  2008-03-23
- Data Source
  KAKENHI-PROJECT-19740041
[Presentation] CI 変形の局所変形への分解について2008
- Author(s)
  田中心
- Organizer
  日本数学会2008 年会「トポロジー分科会」
- Place of Presentation
  近畿大学理工学部
- Data Source
  KAKENHI-PROJECT-19740041
[Presentation] コバノフ理論の幾何的定式化に於ける局所関係式について2008
- Author(s)
  田中心
- Organizer
  日本数学会2008秋季総合分科会「トポロジー分科会」
- Place of Presentation
  東京工業大学
- Data Source
  KAKENHI-PROJECT-19740041
[Presentation] 多重共役カンドルのホモロジーについて
- Author(s)
  Scott Carter, Atsushi Ishii, Masahico Saito, Kokoro Tanaka
- Organizer
  ハンドル体結び目とその周辺VII
- Place of Presentation
  奈良女子大学
- Year and Date
  2014-10-04 – 2014-10-05
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] Regular-equivalence of 2-knot diagrams and sphere eversions
- Author(s)
  Masamichi Takase, Kokoro Tanaka
- Organizer
  A Satellite Conference of Seoul ICM 2014: Knots and Low Dimensional Manifolds
- Place of Presentation
  BEXCO Convention & Exhibition Center II, Busan, Korea
- Year and Date
  2014-08-22 – 2014-08-26
- Data Source
  KAKENHI-PROJECT-26400082
[Presentation] On n-almost positive adequate links
- Author(s)
  Kokoro Tanaka
- Organizer
  2014 琉球結び目セミナー
- Place of Presentation
  那覇市ぶんかテンブス館2階那覇市伝統工芸館会議室
- Year and Date
  2014-06-21 – 2014-06-22
- Data Source
  KAKENHI-PROJECT-26400082

1. 安原晃 (60256625)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
2. GUERVILLE BENOIT

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
3. ISHII Atsushi

# of Collaborated Projects: 0 results

# of Collaborated Products: 1 results
4. 石川勝巳

# of Collaborated Projects: 0 results

# of Collaborated Products: 1 results

Tanaka Kokoro 田中 心

TANAKA Kokoro 田中 心

Research Projects

Research Products

Co-Researchers

曲面結び目とカンドルコサイクル不変量Principal Investigator

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カンドル代数と曲面結び目理論Principal Investigator

Principal Investigator

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Review Section

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Elucidation of the geometric meaning of surface knot invariants defined by quandles and its applicationPrincipal Investigator

Principal Investigator

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複素射影平面上の直線配置と絡み目のミルナー不変量の研究Principal Investigator

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Research Institution

Study of Roseman moves using quandle theory and immersion theoryPrincipal Investigator

Principal Investigator

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Research Institution

Elucidation of diagrammatic properties of surface-knots and construction of new invariants of surface-knotsPrincipal Investigator

Principal Investigator

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Research Field

Research Institution

Research of surface-knots using quandles and Khovanov theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

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Research Field

Research Institution

[Journal Article] Quandle colorings vs. biquandle colorings2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The bridge number of surface links and kei colorings2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Shifting chain maps in quandle homology and cocycle invariants2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Homology for quandles with partial group operations2017

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Regular-equivalence of $2$-knot diagrams and sphere eversions2016

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Independence of Roseman moves including triple points2016

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On rack colorings for surface-knot diagrams without branch points2015

Author(s)

Journal Title

Tanaka Kokoro 田中心

TANAKA Kokoro 田中心