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SAKAI Keiichi｜Shinshu University Researcher List

SAKAI Keiichi

Academic Assembly　School of Science and Technology　Institute of Science

Faculty of Science　Department of Mathematics　Course of Mathematical Sciences　

Professor　

Researcher Information

Field Of Study

  • topology
Research activity information

Paper

  • The Fox-Hatcher cycle and a Vassiliev invariant of order three
    Saki Kanou, Keiichi Sakai
    Pacific Journal of Mathematics, 323(2), 281-306, 02 Jun. 2023, Refereed
    Lead, Corresponding電子ジャーナル
  • Span of the Jones polynomials of certain v-adequate virtual links
    Okamura, Minori; Sakai, Keiichi;
    Journal of Knot Theory and Its Ramifications, 30(1), Jan. 2021リポジトリ電子ジャーナル
  • Generalized connected sum formula for the Arnold invariants of generic plane curves
    Keiichi Sakai, Ryutaro Sugiyama
    Topology and its Applications, 255, 86-108, 28 Jan. 2019電子ジャーナル
  • The space of short ropes and the classifying space of the space of long knots
    Syunji Moriya, Keiichi Sakai
    Algebraic and Geometric Topology, 18(5), 2859-2873, 22 Aug. 2018, Refereed電子ジャーナル
  • BV-structures on the homology of the framed long knot space
    Keiichi Sakai
    Journal of Homotopy and Related Structures, 11(3), 425-441, 01 Sep. 2016, Refereedリポジトリ電子ジャーナル
  • Lin-Wang type formula for Haefliger invariant
    Keiichi Sakai
    Homology, Homotopy and Applications, 17(2), 317-341, 03 Dec. 2015電子ジャーナル
  • Deloopings of the spaces of long embeddings
    Keiichi Sakai
    Fundamenta Mathematicae, 227(1), 27-34, 01 Aug. 2014, Refereedリポジトリ電子ジャーナル
  • 1-loop graphs and configuration space integral for embedding spaces
    Keiichi Sakai and Tadayuki Watanabe
    Mathematical Proceedings of the Cambridge Philosophical Society, 152(Issue 03), 497-533, May 2012WebofScienceリポジトリ電子ジャーナル
  • On a move reducing the genus of a knot diagram
    Kenji Daikoku, Keiichi Sakai and Masamichi Takase
    Indiana UniversityMathematics Journal, 61(3), 1111-1127, 2012, Refereed電子ジャーナル
  • An integral expression of the first non-trivial one-cocycle of the space of longknots in R^3
    Keiichi Sakai
    Pacific Journal of Mathematics, 250(2), 407-419, Apr. 2011WebofScienceリポジトリ電子ジャーナル
  • Configuration space integrals for embedding spaces and the Haefliger invariant
    Keiichi Sakai
    Journal of Knot Theory and Its Ramifications, 19(12), 1597-1644, 2010電子ジャーナル
  • Nontrivalent graph cocycle and the cohomology of long knot space
    Keiichi Sakai
    Algebraic and Geometric Topology, 8(3), 1499-1522, 2008電子ジャーナル
  • Poisson structures on the homology of the space of knots
    Keiichi Sakai
    Geometry and Topology Monographs, 13, 463-482, 2008電子ジャーナル

MISC

  • 三葉結び目
    境 圭一
    数学者の選ぶ「とっておきの数学」, 06 Sep. 2023, Invited
  • Embedding spaces, configuration spaces and Vassiliev invariants
    Keiichi Sakai
    数学, 72(3), 285 - 336, Jul. 2020, Refereed, Invited
    Lead

Lectures, oral presentations, etc.

  • The Fox-Hatcher cycle and a Vassiliev invariant of order three
    Keiichi Sakai
    New Developments in Four Dimensions, 17 Jun. 2022, Invited
  • The Fox-Hatcher cycle and a Vassiliev invariant of order three
    Keiichi Sakai
    Differential Topology Seminar, 17 May 2022, Invited
  • Span of the Jones polynomials of certain v-adequate virtual links
    Keiichi Sakai
    Moscow-Beijing topology seminar (online), 17 Mar. 2021, Invited
  • L-infinity algebras and graph cocycles
    Keiichi Sakai
    Homotopy Theory Symposium, 28 Oct. 2019, Invited
  • Lin-Wang type formula for the Haefliger invariant
    Keiichi Sakai
    Workshop "Spaces of Embeddings: Connections and Applications", 17 Oct. 2019
  • The space of short ropes and the classifying space of the space of long knots
    Keiichi Sakai
    Mapping Spaces in Algebraic Topology, 30 Aug. 2018, Invited
  • The space of short ropes and the classifying space of the space of long knots
    Keiichi Sakai
    The 59th Cascade Topology Seminar, 21 Oct. 2017, Invited
  • Lin-Wang type formula for Haefliger's invariant
    Keiichi Sakai
    11 Aug. 2014, ICM2014 Satellite Conference on Algebraic Topology
  • Deloopings of the spaces of long embeddings
    Keiichi Sakai
    International Conference on Topology and Geometry 2013, 05 Sep. 2013
  • BV-structures on the homology of the framed long knot space
    Keiichi Sakai
    4th East Asian Conference on Algebraic Topology, 09 Dec. 2011
  • 配置空間積分によるHaefliger不変量の表示
    Keiichi Sakai
    日本数学会2009年度秋季総合分科会, 25 Sep. 2009
  • Non-trivalent graph cocycle and the cohomology of the long knot space
    Keiichi Sakai
    日本数学会2008年度秋季総合分科会, 24 Sep. 2008
  • Poisson structure on the homology of the space of framed embeddings
    Keiichi Sakai
    第54回トポロジーシンポジウム, 07 Aug. 2007
  • On the space of all embeddings R^1 ->R^n and loop spaces of configuration spaces
    Keiichi Sakai
    Intelligence of Low Dimensional Topology 2005, 07 Nov. 2005

Affiliated academic society

  • 日本数学会

Research Themes

  • 埋め込みのなす空間のトポロジーと有限型不変量
    科学研究費補助金, 基盤(C)
    01 Apr. 2020 - 31 Mar. 2025
  • 埋め込みのなす空間の位相幾何学から見る，有限型不変量の幾何学的解釈
    科学研究費補助金, 基盤研究(C)
    01 Apr. 2016 - 31 Mar. 2020
  • 幾何学的・代数的トポロジーの手法による埋め込みの空間の研究
    科学研究費補助金, 若手(B)
    01 Apr. 2013 - 31 Mar. 2016
  • 配置空間積分、オペラッド、関手の微積分による埋め込みの空間のトポロジーの研究
    科学研究費補助金, 研究活動スタート支援
    24 Aug. 2011 - 31 Mar. 2013
  • 配置空間積分及びオペラッドの作用を用いた,埋め込みの空間のトポロジーの研究
    科学研究費補助金, 特別研究員奨励費
    01 Apr. 2010 - 31 Mar. 2011
  • 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
    科学研究費補助金, 若手研究(B)
    01 Apr. 2009 - 31 Mar. 2010
  • topology of the embedding spaces

Academic Contribution Activities

  • Planning etc
    Braids, Configuration Spaces and Quantum Topology (2015), Lecture Hall in Graduate School of Mathematical Sciences, The University of Tokyo, 9/10