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
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
- 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
- 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 - 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 - 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 - Lin-Wang type formula for Haefliger invariant
Keiichi Sakai
Homology, Homotopy and Applications, 17(2), 317-341, 03 Dec. 2015 - Deloopings of the spaces of long embeddings
Keiichi Sakai
Fundamenta Mathematicae, 227(1), 27-34, 01 Aug. 2014, Refereed - 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 2012
- 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 - 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. 2011 - Configuration space integrals for embedding spaces and the Haefliger invariant
Keiichi Sakai
Journal of Knot Theory and Its Ramifications, 19(12), 1597-1644, 2010 - Nontrivalent graph cocycle and the cohomology of long knot space
Keiichi Sakai
Algebraic and Geometric Topology, 8(3), 1499-1522, 2008 - Poisson structures on the homology of the space of knots
Keiichi Sakai
Geometry and Topology Monographs, 13, 463-482, 2008
MISC
Lectures, oral presentations, etc.
- Non-trivalent graph cocycles and Vassiliev invariants
Keiichi Sakai
第49回変換群論シンポジウム, 02 Dec. 2023, InvitedGerstenhaber algebra structures on Hochschild homology of cosimplicial space
Keiichi Sakai
多様体と写像空間の代数トポロジー, 19 Nov. 2023, InvitedThe Fox-Hatcher cycle and a Vassiliev invariant of order three
Keiichi Sakai
New Developments in Four Dimensions, 17 Jun. 2022, InvitedThe Fox-Hatcher cycle and a Vassiliev invariant of order three
Keiichi Sakai
Differential Topology Seminar, 17 May 2022, InvitedSpan of the Jones polynomials of certain v-adequate virtual links
Keiichi Sakai
Moscow-Beijing topology seminar (online), 17 Mar. 2021, InvitedL-infinity algebras and graph cocycles
Keiichi Sakai
Homotopy Theory Symposium, 28 Oct. 2019, InvitedLin-Wang type formula for the Haefliger invariant
Keiichi Sakai
Workshop "Spaces of Embeddings: Connections and Applications", 17 Oct. 2019The space of short ropes and the classifying space of the space of long knots
Keiichi Sakai
Mapping Spaces in Algebraic Topology, 30 Aug. 2018, InvitedThe space of short ropes and the classifying space of the space of long knots
Keiichi Sakai
The 59th Cascade Topology Seminar, 21 Oct. 2017, InvitedLin-Wang type formula for Haefliger's invariant
Keiichi Sakai
11 Aug. 2014, ICM2014 Satellite Conference on Algebraic TopologyDeloopings of the spaces of long embeddings
Keiichi Sakai
International Conference on Topology and Geometry 2013, 05 Sep. 2013BV-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. 2009Non-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. 2008Poisson 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. 2007On 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. 2005Research 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
- 空間の代数的・幾何的モデルとその周辺(2024)
Planning etc
信州大学理学部（オンラインとのハイブリッド）, 26 Aug. 2024 - 28 Aug. 2024 - 空間の代数的・幾何的モデルとその周辺(2023)
Planning etc
信州大学理学部（オンラインとのハイブリッド）, 15 Sep. 2023 - 17 Sep. 2023 - 空間の代数的・幾何的モデルとその周辺(2022)
Planning etc
信州大学理学部（オンラインとのハイブリッド）, 31 Aug. 2022 - 02 Sep. 2022 - Braids, Configuration Spaces and Quantum Topology (2015)
Planning etc
Lecture Hall in Graduate School of Mathematical Sciences, The University of Tokyo, 07 Sep. 2015 - 10 Sep. 2015
