Ishii Atsushi 石井敦

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ISHII Atsushi 石井敦

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Researcher Number	00531451
Other IDs
Affiliation (Current)	2025: 筑波大学, 数理物質系, 准教授
Affiliation (based on the past Project Information) *help	2019 – 2023: 筑波大学, 数理物質系, 准教授 2013 – 2018: 筑波大学, 数理物質系, 講師 2011 – 2012: 筑波大学, 数理物質系, 助教 2009 – 2010: University of Tsukuba, 大学院・数理物質科学研究科, 助教
Review Section/Research Field	Principal Investigator Geometry / Basic Section 11020:Geometry-related Except Principal Investigator Geometry
Keywords	Principal Investigator 結び目理論 / 位相幾何学 Except Principal Investigator 色分け（彩色） / 周期点 / 位相エントロピー / 等長変換 / 位相空間 / 連続体 / フラクタル / 位相次元 … More / 色彩問題 / 連続体論 / フラクタル次元 / アトラクター / 幾何学的トポロジー / 位相力学系 / エントロピー / カオス / 彩色数 / 単体複体 / Whitney位相 / 同相写像群 / 無限充満複体 / 距離位相 / (ホワイトヘッド)弱位相 / 箱積,箱位相 / 帰納的極限 / LF空間,LF多様体 / コンパクト化 / 擬内部 / ヒルベルト・キューブ / 関数空間 / LF空間 / フレッシェ空間 / 帰納極限 / 無限次元多様体 / 位相幾何学 Less

Geometry of handlebody-knotsPrincipal Investigator
- Principal Investigator
  
  石井敦
- Project Period (FY)
  2021 – 2025
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  University of Tsukuba
Handlebody-knots and augmented Alexander invariantsPrincipal Investigator
- Principal Investigator
  
  Ishii Atsushi
- Project Period (FY)
  2018 – 2021
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  University of Tsukuba
Orientations and invariants of handlebody-knotsPrincipal Investigator
- Principal Investigator
  
  ISHII Atsushi
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
Study of dynamical systems by use of general topology and geometric topology
- Principal Investigator
  
  KATO HISAO
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
Handlebody-knots and invariantsPrincipal Investigator
- Principal Investigator
  
  ISHII Atsushi
- Project Period (FY)
  2012 – 2014
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
Topology of Infinite-Dimensional Manifolds and Inductive Limits
- Principal Investigator
  
  SAKAI Katsuro
- Project Period (FY)
  2010 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
Handlebody-knots and topologyPrincipal Investigator
- Principal Investigator
  
  ISHII Atsushi
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba

All 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2012 2011 2010 2009 Other

All Journal Article Presentation

[Journal Article] The fundamental multiple conjugation quandle of a handlebody-link2022
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Journal of the Mathematical Society of Japan
  
  Volume: 74 Issue: 1 Pages: 1-23
- DOI
  10.2969/jmsj/84308430
- NAID
  130008144189
- ISSN
  0025-5645, 1881-1167, 1881-2333
- Language
  English
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03217
[Journal Article] QUANDLE TWISTED ALEXANDER INVARIANTS2022
- Author(s)
  Atsushi Ishii and Kanako Oshiro
- Journal Title
  
  Osaka Journal of Mathematics
  
  Volume: 59 Issue: 3 Pages: 683-702
- DOI
  10.18910/88492
- ISSN
  00306126
- URL
  https://ocu-omu.repo.nii.ac.jp/records/2010891
- Language
  English
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03217
[Journal Article] Derivatives with Alexander pairs for quandles2022
- Author(s)
  Atsushi Ishii and Kanako Oshiro
- Journal Title
  
  Fund. Math.
  
  Volume: 259 Issue: 1 Pages: 1-31
- DOI
  10.4064/fm890-12-2021
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03217
[Journal Article] Row relations of twisted Alexander matrices and shadow quandle 2-cocycles2021
- Author(s)
  Ishii Atsushi、Oshiro Kanako
- Journal Title
  
  Topology and its Applications
  
  Volume: 301 Pages: 107513-107513
- DOI
  10.1016/j.topol.2020.107513
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03292
[Journal Article] Cocycles of G-Alexander biquandles and G-Alexander multiple conjugation biquandles2021
- Author(s)
  Ishii Atsushi、Iwakiri Masahide、Kamada Seiichi、Kim Jieon、Matsuzaki Shosaku、Oshiro Kanako
- Journal Title
  
  Topology and its Applications
  
  Volume: 301 Pages: 107512-107512
- DOI
  10.1016/j.topol.2020.107512
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03292, KAKENHI-PROJECT-19H01788, KAKENHI-PROJECT-18K03306, KAKENHI-PROJECT-17H06128
[Journal Article] A multiple group rack and oriented spatial surfaces2020
- Author(s)
  Atsushi Ishii, Shosaku Matsuzaki and Tomo Murao
- Journal Title
  
  J. Knot Theory Ramifications
  
  Volume: 29 Issue: 07 Pages: 2050046-2050046
- DOI
  10.1142/s0218216520500467
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03292, KAKENHI-PROJECT-20K22312
[Journal Article] Biquandle (co)homology and handlebody-links2018
- Author(s)
  Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro
- Journal Title
  
  J. Knot Theory Ramifications
  
  Volume: 27 Issue: 11 Pages: 1843011-1843011
- DOI
  10.1142/s0218216518430113
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03292, KAKENHI-PROJECT-17H06128, KAKENHI-PROJECT-26287013
[Journal Article] A multiple conjugation biquandle and handlebody-links2018
- Author(s)
  Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro
- Journal Title
  
  Hiroshima Math. J.
  
  Volume: 48 Pages: 89-117
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04866
[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] The Markov theorems for spatial graphs and handlebody-knots with Y-orientations2015
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Internat. J. Math.
  
  Volume: 26 Issue: 14 Pages: 1550116-1550116
- DOI
  10.1142/s0129167x15501165
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04866
[Journal Article] A multiple conjugation quandle and handlebody-knots2015
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Topology Appl.
  
  Volume: 196 Pages: 492-500
- DOI
  10.1016/j.topol.2015.05.029
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04866
[Journal Article] Handlebody-knot invariants derived from unimodular Hopf algebras2014
- Author(s)
  Atsushi Ishii, Akira Masuoka
- Journal Title
  
  J. Knot Theory Ramifications
  
  Volume: 23 Issue: 07 Pages: 1460001-1460024
- DOI
  10.1142/s0218216514600013
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-24740037, KAKENHI-PROJECT-26400035
[Journal Article] A table of genus two handlebody-knots up to six crossings2012
- Author(s)
  Atsushi Ishii, Kengo Kishimoto, Hiromasa Moriuchi, Masaaki Suzuki
- Journal Title
  
  J. Knot Theory Ramifications
  
  Volume: ２１ Issue: 04 Pages: 1250035-1250035
- DOI
  10.1142/s0218216511009893
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24740037
[Journal Article] Quandle cocycle invariants for spatial graphs and knotted handlebodies2012
- Author(s)
  Atsushi Ishii, Masahide Iwakiri
- Journal Title
  
  Canad. J. Math.
  
  Volume: ６４ Pages: 102-122
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24740037
[Journal Article] A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map2012
- Author(s)
  Atsushi Ishii, Kengo Kishimoto
- Journal Title
  
  Topology Appl.
  
  Volume: １５９ Issue: 4 Pages: 1115-1121
- DOI
  10.1016/j.topol.2011.11.018
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24740037
[Journal Article] An operator invariant for handlebody-knots2012
- Author(s)
  Kai Ishihara, Atsushi Ishii
- Journal Title
  
  Fund. Math.
  
  Volume: ２１７ Issue: 3 Pages: 233-247
- DOI
  10.4064/fm217-3-3
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24740037
[Journal Article] On normalizations of a regular isotopy invariant for spatial graphs2011
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Internat. J. Math
  
  Volume: 22 Issue: 11 Pages: 1545-1559
- DOI
  10.1142/s0129167x1100729x
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The quandle coloring invariant of a reducible handlebody-knot2011
- Author(s)
  Atsushi Ishii, Kengo Kishimoto
- Journal Title
  
  Tsukuba J.Math.
  
  Volume: 35 Pages: 131-141
- NAID
  120006312315
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The quandle coloring invariant of a reducible handlebody-knot2011
- Author(s)
  Atsushi Ishii, Kengo Kishimoto
- Journal Title
  
  Tsukuba J. Math
  
  Volume: 35 Pages: 131-141
- NAID
  120006312315
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The leading finite type coefficients of the Links-Gould polynomial of a link2010
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Kyungpook Math. J
  
  Volume: 50 Pages: 49-58
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The Miyazawa polynomial for long virtual knots2010
- Author(s)
  Atsushi Ishii, Naoko Kamada, Seiichi Kamada
- Journal Title
  
  Topology Appl. 157
  
  Pages: 290-297
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The IH-complex of spatial trivalent graphs2010
- Author(s)
  Atsushi Ishii, Kengo Kishimoto
- Journal Title
  
  Tokyo J.Math.
  
  Volume: 33 Pages: 523-535
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The leading finite type coefficients of the Links-Gould polynomial of a link2010
- Author(s)
  Atsushi Ishii
- Journal Title
  
  Kyungpook Math.J.
  
  Volume: 50 Pages: 49-58
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The IH-complex of spatial trivalent graphs2010
- Author(s)
  Atsushi Ishii, Kengo Kishimoto
- Journal Title
  
  Tokyo J. Math
  
  Volume: 33 Issue: 2 Pages: 523-535
- DOI
  10.3836/tjm/1296483486
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Journal Article] The Miyazawa polynomial for long virtual knots2010
- Author(s)
  Atsushi Ishii, Naoko Kamada, Seiichi Kamada
- Journal Title
  
  Topology Appl
  
  Volume: 157 Issue: 1 Pages: 290-297
- DOI
  10.1016/j.topol.2009.04.058
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Alexander type invariants of groups, quandles and MCQs2023
- Author(s)
  石井敦
- Organizer
  日本数学会年会
- Invited
- Data Source
  KAKENHI-PROJECT-21K03217
[Presentation] Quandle twisted Alexander invariants with cohomologous Alexander pairs2023
- Author(s)
  石井敦
- Organizer
  数理情報科学セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-21K03217
[Presentation] On a quandle derivative2020
- Author(s)
  石井敦
- Organizer
  カンドルと対称空間
- Invited
- Data Source
  KAKENHI-PROJECT-18K03292
[Presentation] Fox derivatives for quandles2019
- Author(s)
  石井敦
- Organizer
  日本数学会年会
- Data Source
  KAKENHI-PROJECT-18K03292
[Presentation] Generalized quandle cocycle invariants and shadow quandle cocycle invariants2019
- Author(s)
  Atsushi Ishii
- Organizer
  The Third Pan Pacific International Conference on Topology and Applications
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03292
[Presentation] An augmented Alexander matrix and an affine extension of a quandle2018
- Author(s)
  Atsushi Ishii
- Organizer
  Branched Coverings, Degenerations, and Related Topics 2018
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04866
[Presentation] Parallel biquandle colorings for handlebody-knots and spatial graphs2016
- Author(s)
  Atsushi Ishii
- Organizer
  International Workshop on Spatial Graphs 2016
- Place of Presentation
  早稲田大学（東京都新宿区）
- Year and Date
  2016-08-03
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04866
[Presentation] The skein index and Fox p-colorings2015
- Author(s)
  Atsushi Ishii
- Organizer
  Knots and Manifolds
- Place of Presentation
  大阪市立大学
- Year and Date
  2015-02-07
- Invited
- Data Source
  KAKENHI-PROJECT-24740037
[Presentation] The Markov theorem for spatial graphs and handlebody-knots2015
- Author(s)
  Atsushi Ishii
- Organizer
  AMS Sectional Meeting
- Place of Presentation
  California State University (U.S.A)
- Year and Date
  2015-10-24
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04866
[Presentation] Invariants for handlebody-knots derived from Yetter-Drinfeld modules2012
- Author(s)
  Atsushi Ishii
- Organizer
  The 8th East Asian School of Knots and Related Topics, Korea Advanced Institute of Science and Technology
- Place of Presentation
  Daejeon, Korea
- Year and Date
  2012-01-11
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] An introduction to handlebody-knot theory, Colloquium2012
- Author(s)
  Atsushi Ishii
- Place of Presentation
  The University of South Florida, The United States of America
- Year and Date
  2012-02-13
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Quantum-commutative quantum-symmetric algebras and invariants for handlebody-links2012
- Author(s)
  Atsushi Ishii
- Organizer
  日本数学会年会
- Place of Presentation
  東京理科大学
- Year and Date
  2012-03-26
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] A quandle cocycle invariant with non-commutative flows for a handle body-knot2011
- Author(s)
  石井敦
- Organizer
  Intelligence of Low-dimensional Topology
- Place of Presentation
  京都大学(京都市)(招待講演)
- Year and Date
  2011-05-27
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Quandle colorings with non-commutative flows2011
- Author(s)
  Atsushi Ishii
- Organizer
  トポロジー火曜セミナー
- Place of Presentation
  東京大学
- Year and Date
  2011-05-17
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] 非可換フローを用いたハンドル体結び目のカンドルコサイクル不変量2011
- Author(s)
  Atsushi Ishii
- Organizer
  Knotting Nagoya
- Place of Presentation
  名古屋市立大学
- Year and Date
  2011-02-19
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] A handlebody-knot and a Yetter-Drinfeld module2011
- Author(s)
  Atsushi Ishii
- Organizer
  結び目の量子不変量とそのカテゴリー化
- Place of Presentation
  早稲田大学
- Year and Date
  2011-08-26
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] A quandle cocycle invariant with non-commutative flows for a handlebody-knot2011
- Author(s)
  Atsushi Ishii
- Organizer
  Intelligence of Low-dimensional Topology
- Place of Presentation
  京都大学
- Year and Date
  2011-05-27
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] A quandle cocycle invariant on a group representation for handlebody-links I, II2011
- Author(s)
  Atsushi Ishii, Yeonhee Jang, Kanako Oshiro
- Organizer
  The Seventh East Asian School of Knots and Related Topics
- Place of Presentation
  広島大学
- Year and Date
  2011-01-10
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] On normalizations of a regular isotopy invariant for spatial graphs2010
- Author(s)
  Atsushi Ishii
- Organizer
  日本数学会年会
- Place of Presentation
  慶應義塾大学
- Year and Date
  2010-03-26
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Normalizations for the Yamada polynomial2010
- Author(s)
  Atsushi Ishii
- Organizer
  The Sixth East Asian School of Knots and Related Topics
- Place of Presentation
  Nankai University, Tianjin, China
- Year and Date
  2010-01-26
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] A knotted handlebody and a spatial graph2010
- Author(s)
  Atsushi Ishii
- Organizer
  International Workshop on Spatial Graphs 2010
- Place of Presentation
  早稲田大学
- Year and Date
  2010-08-19
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] ハンドル体絡み目の有限型不変量2010
- Author(s)
  Atsushi Ishii
- Organizer
  ハンドル体結び目とその周辺III
- Place of Presentation
  東京女子大学
- Year and Date
  2010-05-15
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Invariants for knotted handlebodies2010
- Author(s)
  Atsushi Ishii
- Organizer
  量子群と量子トポロジー
- Place of Presentation
  京都大学
- Year and Date
  2010-04-20
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] The IH-complex of spatial trivalent graphs I2009
- Author(s)
  石井敦
- Organizer
  日本数学会秋季総合分科会
- Place of Presentation
  大阪大学
- Year and Date
  2009-09-25
- Data Source
  KAKENHI-PROJECT-21740035
[Presentation] Multiple conjugation quandles and handlebody-knots
- Author(s)
  Atsushi Ishii
- Organizer
  2013 TAPU Workshop on Knot Theory and Related Topics, National Institute for Mathematical Sciences
- Place of Presentation
  Daejeon, Korea
- Invited
- Data Source
  KAKENHI-PROJECT-24740037

1. KAWAMURA Kazuhiro (40204771)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
2. KATO Hisao (70152733)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
3. SAKAI Katsuro (50036084)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
4. YAGASAKI Tasuhiko (40191077)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
5. MINE Kotaro (90512525)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
6. KANETO Takeshi (70107340)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
7. TANGE Motoo (70452422)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

Ishii Atsushi 石井 敦

ISHII Atsushi 石井 敦

Research Projects

Research Products

Co-Researchers

Geometry of handlebody-knotsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Handlebody-knots and augmented Alexander invariantsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Orientations and invariants of handlebody-knotsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Study of dynamical systems by use of general topology and geometric topology

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Handlebody-knots and invariantsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Topology of Infinite-Dimensional Manifolds and Inductive Limits

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Handlebody-knots and topologyPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] The fundamental multiple conjugation quandle of a handlebody-link2022

Author(s)

Journal Title

DOI

NAID

ISSN

Language

Data Source

[Journal Article] QUANDLE TWISTED ALEXANDER INVARIANTS2022

Author(s)

Journal Title

DOI

ISSN

URL

Language

Data Source

[Journal Article] Derivatives with Alexander pairs for quandles2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Row relations of twisted Alexander matrices and shadow quandle 2-cocycles2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Cocycles of G-Alexander biquandles and G-Alexander multiple conjugation biquandles2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] A multiple group rack and oriented spatial surfaces2020

Author(s)

Ishii Atsushi 石井敦

ISHII Atsushi 石井敦