Sakai Keiichi 境圭一

… Alternative Names

SAKAI Keiichi 境圭一

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Researcher Number	20466824
Other IDs
Affiliation (Current)	2025: 信州大学, 学術研究院理学系, 教授
Affiliation (based on the past Project Information) *help	2022 – 2025: 信州大学, 学術研究院理学系, 教授 2016 – 2022: 信州大学, 学術研究院理学系, 准教授 2014 – 2015: 信州大学, 学術研究院理学系, 助教 2011 – 2013: 信州大学, 理学部, 助教 2010: The University of Tokyo, 数理(科)学研究科(研究院), その他 2009: The University of Tokyo, 大学院・数理科学研究科, 特任研究員
Review Section/Research Field	Principal Investigator Geometry / Basic Section 11020:Geometry-related Except Principal Investigator Basic Section 11020:Geometry-related / Geometry
Keywords	Principal Investigator 埋め込みの空間 / グラフ / オペラッド / 配置空間積分 / 配置空間 / グラフ複体 / 有限型不変量 / 埋め込みのなす空間 / Haefliger不変量 / 多重ループ空間 … More / 分類空間 / 代数的トポロジー / ループ空間 / Hochschildホモロジー / Vassiliev不変量 / 多様体解析 / 特性類 / Gerstenhaber代数 / Operad / operad / Gramainサイクル / Fox-Hatcherサイクル / Hochschild複体 / ジェネリック平面曲線 / 幾何学的トポロジー / 群完備化 / 双対構成 / Lie環のコホモロジー / 埋め込みの空間の位相幾何学 / L無限代数 / ジェネリックはめ込み / トポロジー / 関手の微積分 / BV代数 / ストリング・トポロジー / 位相的Stiefel多様体 … More Except Principal Investigator 開閉位相的場の理論 / ループ積 / 弦作用素 / de Rham ホモトピー / Cartan カルキュラス / 微分代数モデル / ディフェオロジー / ストリングトポロジー / 結び目 / 位相不変量 / ファインマンダイアグラム / 同変不変量 / 有理ホモトピー群 / 微分同相群 / ３次元多様体 / 有限型不変量 / Morse理論 / Chern-Simons摂動理論 Less

New perspectives of the embedding spaces and the finite type invariants through a fusion of configuration space integrals and manifold calculusPrincipal Investigator
- Principal Investigator
  
  境圭一
- Project Period (FY)
  2025 – 2029
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Shinshu University
The investigation of the non-triviality of string topology in a topological quantum field theory and differentiable stacks
- Principal Investigator
  
  栗林勝彦
- Project Period (FY)
  2021 – 2025
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Shinshu University
Topology of the embedding spaces and the finite type invariantsPrincipal Investigator
- Principal Investigator
  
  境圭一
- Project Period (FY)
  2020 – 2024
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Shinshu University
An interpretation of finite type invariants from the viewpoint of the topology of embedding spacesPrincipal Investigator
- Principal Investigator
  
  Sakai Keiichi
- Project Period (FY)
  2016 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Shinshu University
Morse theory and topology of manifolds / groups of diffeomorphisms
- Principal Investigator
  
  Watanabe Tadayuki
- Project Period (FY)
  2014 – 2017
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Shimane University
Geometric and algebraic approach to the embedding spacesPrincipal Investigator
- Principal Investigator
  
  SAKAI Keiichi
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Shinshu University
Topology of the embedding spaces via configuration space integrals, operads and the calculus of functorsPrincipal Investigator
- Principal Investigator
  
  SAKAI Keiichi
- Project Period (FY)
  2011 – 2012
- Research Category
  
  Grant-in-Aid for Research Activity Start-up
- Research Field
  
  Geometry
- Research Institution
  Shinshu University
配置空間積分とオペラッドを用いた,埋め込みの空間の位相幾何学Principal Investigator
- Principal Investigator
  
  境圭一
- Project Period (FY)
  2009 – 2010
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  The University of Tokyo

All 2023 2022 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 Other

All Journal Article Presentation

[Journal Article] The Fox-Hatcher cycle and a Vassiliev invariant of order three2023
- Author(s)
  Saki Kanou, Keiichi Sakai
- Journal Title
  
  Pacific Journal of Mathematics
  
  Volume: 323 Issue: 2 Pages: 281-306
- DOI
  10.2140/pjm.2023.323.281
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-20K03608, KAKENHI-PROJECT-23K20795
[Journal Article] Generalized connected sum formula for the Arnold invariants of generic plane curves2019
- Author(s)
  Keiichi Sakai, Ryutaro Sugiyama
- Journal Title
  
  Topology and its Applications
  
  Volume: 255 Pages: 86-108
- DOI
  10.1016/j.topol.2018.12.010
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K05144
[Journal Article] The space of short ropes and the classifying space of the space of long knots2018
- Author(s)
  Syunji Moriya, Keiichi Sakai
- Journal Title
  
  Algebraic and Geometric Topology
  
  Volume: 18 Issue: 5 Pages: 2859-2873
- DOI
  10.2140/agt.2018.18.2859
- NAID
  120007173398
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K05144
[Journal Article] The space of short ropes and the classifying space of the space of long knots2018
- Author(s)
  Syunji Moriya and Keiichi Sakai
- Journal Title
  
  Algebraic and Geometric Topology
  
  Volume: 印刷中
- NAID
  120007173398
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K05144
[Journal Article] BV-structures on the homology of the framed long knot space2016
- Author(s)
  Keiichi Sakai
- Journal Title
  
  Journal of Homotopy and Related Structures (Online First Article)
  
  Volume: 11 Issue: 3 Pages: 1-17
- DOI
  10.1007/s40062-015-0111-1
- NAID
  120007100728
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-25800038
[Journal Article] Lin-Wang type formula for the Haefliger invariant2015
- Author(s)
  Keiichi Sakai
- Journal Title
  
  Homology, Homotopy and Applications
  
  Volume: 17 Issue: 2 Pages: 317-341
- DOI
  10.4310/hha.2015.v17.n2.a15
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-25800038
[Journal Article] Deloopings of the spaces of long embeddings2014
- Author(s)
  Keiichi Sakai
- Journal Title
  
  Fundamenta Mathematicae
  
  Volume: 227 Issue: 1 Pages: 27-34
- DOI
  10.4064/fm227-1-3
- NAID
  120007100729
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-25800038
[Journal Article] 1-loop graphs and configuration space integral for embedded spaces2012
- Author(s)
  Keiichi Sakai, Tadayuki Watanabe
- Journal Title
  
  Mathematical Proceedings of the Cambridge Philosophical Society
  
  Volume: 152 Issue: 3 Pages: 497-533
- DOI
  10.1017/s0305004111000429
- NAID
  120005228644
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20340008, KAKENHI-PROJECT-23740040, KAKENHI-PROJECT-23840015
[Journal Article] Configuration space integrals for embedding spaces and the Haefliger invariant
- Author(s)
  Keiichi Sakai
- Journal Title
  
  Journal of Knot Theory and Its Ramifications (掲載確定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] Non-trivalent graph cocycles and Vassiliev invariants2023
- Author(s)
  境圭一
- Organizer
  第49回変換群論シンポジウム
- Invited
- Data Source
  KAKENHI-PROJECT-23K20795
[Presentation] Gerstenhaber algebra structures on Hochschild homology of cosimplicial space2023
- Author(s)
  境圭一
- Organizer
  多様体と写像空間の代数トポロジー
- Invited
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] Gerstenhaber algebra structures on Hochschild homology of cosimplicial space2023
- Author(s)
  境圭一
- Organizer
  多様体と写像空間の代数トポロジー
- Invited
- Data Source
  KAKENHI-PROJECT-23K20795
[Presentation] Non-trivalent graph cocycles and Vassiliev invariants2023
- Author(s)
  境圭一
- Organizer
  第49回変換群論シンポジウム
- Invited
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] The Fox-Hatcher cycle and a Vassiliev invariant of order three2022
- Author(s)
  境圭一
- Organizer
  日本数学会2022年度秋季総合分科会
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] Some cycles of the space of framed long knots and the Vassiliev invariants2022
- Author(s)
  境圭一
- Organizer
  空間の代数的・幾何的モデルとその周辺
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] The Fox-Hatcher cycle and a Vassiliev invariant of order three2022
- Author(s)
  Keiichi Sakai
- Organizer
  New Developments in Four Dimensions
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] The Fox-Hatcher cycle and a Vassiliev invariant of order three2022
- Author(s)
  境圭一
- Organizer
  微分トポロジーセミナー
- Invited
- Data Source
  KAKENHI-PROJECT-20K03608
[Presentation] L-infinity algebras and graph cocycles2019
- Author(s)
  境圭一
- Organizer
  ホモトピー論シンポジウム2019
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] Lin-Wang type formula for the Haefliger invariant2019
- Author(s)
  Keiichi Sakai
- Organizer
  Spaces of Embeddings: Connections and Applications
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] Lin-Wang type formula for Haefliger's invariant2018
- Author(s)
  境圭一
- Organizer
  トポロジー金曜セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2018
- Author(s)
  境圭一
- Organizer
  第65回トポロジーシンポジウム
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] Generic閉曲線の一般化された連結和に対するArnold不変量の公式2017
- Author(s)
  境圭一
- Organizer
  日本数学会2017年度秋季総合分科会
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2017
- Author(s)
  Keiichi Sakai
- Organizer
  The 59th Cascade Topology Seminar
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2017
- Author(s)
  境圭一
- Organizer
  京都大学代数トポロジーセミナー
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2017
- Author(s)
  境圭一
- Organizer
  東京大学トポロジー火曜セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2017
- Author(s)
  境圭一
- Organizer
  信州トポロジーセミナー
- Invited
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] The space of short ropes and the classifying space of the space of long knots2016
- Author(s)
  境圭一
- Organizer
  研究集会「結び目の数学IX」
- Place of Presentation
  日本大学理学部
- Year and Date
  2016-12-22
- Data Source
  KAKENHI-PROJECT-16K05144
[Presentation] Delooping of the space of long embeddings2015
- Author(s)
  境圭一
- Organizer
  トポロジー金曜セミナー
- Place of Presentation
  九州大学
- Year and Date
  2015-11-06
- Data Source
  KAKENHI-PROJECT-25800038
[Presentation] Haefliger不変量に対するLin-Wang型公式2014
- Author(s)
  境圭一
- Organizer
  日本数学会 2014年度秋季総合分科会
- Place of Presentation
  広島大学
- Year and Date
  2014-09-27
- Data Source
  KAKENHI-PROJECT-25800038
[Presentation] Lin-Wang type formula for Haefliger's invariant2014
- Author(s)
  境圭一
- Organizer
  京都大学談話会
- Place of Presentation
  京都大学
- Year and Date
  2014-12-03
- Invited
- Data Source
  KAKENHI-PROJECT-25800038
[Presentation] Haefliger不変量に対するLin-Wang型公式2014
- Author(s)
  境圭一
- Organizer
  信州トポロジーセミナー
- Place of Presentation
  信州大学
- Year and Date
  2014-04-17
- Data Source
  KAKENHI-PROJECT-25800038
[Presentation] 結び目の種数を減らすある変形について2013
- Author(s)
  境圭一
- Organizer
  Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications
- Place of Presentation
  名城大学名駅サテライト
- Year and Date
  2013-03-02
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] 枠つきlong embeddingの空間のdeloopingについて2013
- Author(s)
  境圭一
- Organizer
  幾何学セミナー
- Place of Presentation
  首都大学東京
- Year and Date
  2013-01-11
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] BV structures on the homology of the framed long embedding spaces2012
- Author(s)
  境圭一
- Organizer
  空間の代数的・幾何的モデルとその周辺
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2012-09-11
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] Embedding spaces and string topology2012
- Author(s)
  境圭一
- Organizer
  講演会
- Place of Presentation
  東京大学大学院数理科学研究科
- Year and Date
  2012-05-08
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] BV-structures on the homology of the framed long knot space2011
- Author(s)
  Keiichi Sakai
- Organizer
  The Fourth East Asian Conference on Algebraic Topology
- Place of Presentation
  東京大学大学院数理科学研究科(招待講演)
- Year and Date
  2011-12-09
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] BV-structures on the homology of the framed long knot space2011
- Author(s)
  Keiichi Sakai
- Organizer
  4th East Asian Conference on Algebraic Topology
- Place of Presentation
  東京大学大学院数理科学研究科
- Year and Date
  2011-12-09
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] Cycles of the spaces of long embeddings arising from the simplest chord diagram2010
- Author(s)
  Keiichi Sakai
- Organizer
  Mini-Workshop "Topology of the Space of Knots"
- Place of Presentation
  東京大学大学院数理科学研究科
- Year and Date
  2010-02-17
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] 配置空間積分と long embedding の空間のコホモロジー2009
- Author(s)
  境圭一
- Organizer
  トポロジー火曜セミナー発表者
- Place of Presentation
  東京大学大学院数理科学研究科
- Year and Date
  2009-05-26
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] Graph complexes, configuration space integral and cohomology of the space of long embeddings2009
- Author(s)
  境圭一
- Organizer
  空間の代数的・幾何的モデルとその周辺2009
- Place of Presentation
  信州大学
- Year and Date
  2009-09-11
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] Non-trivalent graph cocycle, little disks operad and cohomology of the space of long k2009
- Author(s)
  境圭一
- Organizer
  トポロジー金曜セミナー
- Place of Presentation
  九州大学大学院数理学研究院
- Year and Date
  2009-12-11
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] Non-trivalent graph cocycle, little disks operad and cohomology of the space of long k2009
- Author(s)
  境圭一
- Organizer
  微分トポロジーセミナー
- Place of Presentation
  京都大学理学部
- Year and Date
  2009-11-17
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] 配置空間積分による Haefliger 不変量の表示2009
- Author(s)
  境圭一
- Organizer
  日本数学会2009年度秋季総合分科会(一般講演)
- Place of Presentation
  大阪大学
- Year and Date
  2009-09-25
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] Configuration space integrals and the Haefliger invarinat2009
- Author(s)
  境圭一
- Organizer
  トポロジーセミナー東京工業大学
- Place of Presentation
  東京工業大学
- Year and Date
  2009-05-13
- Data Source
  KAKENHI-PROJECT-21740038
[Presentation] 枠つきlong embeddingの空間のdeloopingについて
- Author(s)
  境圭一
- Organizer
  幾何学セミナー
- Place of Presentation
  首都大学東京
- Invited
- Data Source
  KAKENHI-PROJECT-23840015
[Presentation] Embedding spaces and string topology
- Author(s)
  境圭一
- Organizer
  講演会
- Place of Presentation
  東京大学大学院数理科学研究科
- Invited
- Data Source
  KAKENHI-PROJECT-23840015

1. Watanabe Tadayuki (70467447)

# of Collaborated Projects: 1 results

# of Collaborated Products: 1 results
2. SHIMIZU Tatsuro (00738859)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
3. 栗林勝彦 (40249751)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

Sakai Keiichi 境 圭一

SAKAI Keiichi 境 圭一

Research Projects

Research Products

Co-Researchers

New perspectives of the embedding spaces and the finite type invariants through a fusion of configuration space integrals and manifold calculusPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

The investigation of the non-triviality of string topology in a topological quantum field theory and differentiable stacks

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Topology of the embedding spaces and the finite type invariantsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

An interpretation of finite type invariants from the viewpoint of the topology of embedding spacesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Morse theory and topology of manifolds / groups of diffeomorphisms

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Geometric and algebraic approach to the embedding spacesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Topology of the embedding spaces via configuration space integrals, operads and the calculus of functorsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

配置空間積分とオペラッドを用いた,埋め込みの空間の位相幾何学Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] The Fox-Hatcher cycle and a Vassiliev invariant of order three2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Generalized connected sum formula for the Arnold invariants of generic plane curves2019

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The space of short ropes and the classifying space of the space of long knots2018

Author(s)

Journal Title

DOI

NAID

Data Source

[Journal Article] The space of short ropes and the classifying space of the space of long knots2018

Author(s)

Journal Title

NAID

Data Source

[Journal Article] BV-structures on the homology of the framed long knot space2016

Author(s)

Journal Title

DOI

NAID

Data Source

Sakai Keiichi 境圭一

SAKAI Keiichi 境圭一