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SAKAI Keiichi

Academic OrganizationAcademic Assembly School of Science and Technology Institute of ScienceTEL
Education and Research OrganizationFaculty of Science Department of MathematicsFAX
PositionAssociate ProfessorMail Address
Address3-1-1, Asahi, Matsumoto City 390-8621Web sitehttp://math.shinshu-u.ac.jp/~ksakai/index.html

Profile

Research Field
topology
Current Subject
topology of the embedding spaces
Keywords:embeddings , graphs , operads

Research

Books, Articles, etc.
Articles
Generalized connected sum formula for the Arnold invariants of generic plane curves
Topology and its Applications,255:86-108 2019(Jan. 28)
Author:Keiichi Sakai, Ryutaro Sugiyama
Keywords:Generic closed plane curves; The Arnold invariants; Generalized connected sums


The space of short ropes and the classifying space of the space of long knots
Algebraic and Geometric Topology,18(5):2859-2873 2018(Aug. 22)
Author:Syunji Moriya, Keiichi Sakai
Keywords:topological category of long knots, the space of short ropes, classifying space, group completions, spaces of manifolds


BV-structures on the homology of the framed long knot space
Journal of Homotopy and Related Structures,11(3):425-441 2016(Sep. 01)
Author:Keiichi Sakai


Lin-Wang type formula for Haefliger invariant
Homology, Homotopy and Applications,17(2):317-341 2015(Dec. 03)
Author:Keiichi Sakai


Deloopings of the spaces of long embeddings
Fundamenta Mathematicae,227(1):27-34 2014(Aug. 01)
Author:Keiichi Sakai


1-loop graphs and configuration space integral for embedding spaces
Mathematical Proceedings of the Cambridge Philosophical Society,152(Issue 03):497-533 2012(May)
Author:Keiichi Sakai and Tadayuki Watanabe


On a move reducing the genus of a knot diagram
Indiana UniversityMathematics Journal,61(3):1111-1127 2012
Author:Kenji Daikoku, Keiichi Sakai and Masamichi Takase


An integral expression of the first non-trivial one-cocycle of the space of longknots in R^3
Pacific Journal of Mathematics,250(2):407-419 2011(Apr.)
Author:Keiichi Sakai


Configuration space integrals for embedding spaces and the Haefliger invariant
Journal of Knot Theory and Its Ramifications,19(12):1597-1644 2010
Author:Keiichi Sakai


Poisson structures on the homology of the space of knots
Geometry and Topology Monographs,13:463-482 2008
Author:Keiichi Sakai


Nontrivalent graph cocycle and the cohomology of long knot space
Algebraic and Geometric Topology,8(3):1499-1522 2008
Author:Keiichi Sakai


Presentations
Lin-Wang type formula for the Haefliger invariant
Workshop "Spaces of Embeddings: Connections and Applications" 2019(Oct. 17)
Author:Keiichi Sakai


The space of short ropes and the classifying space of the space of long knots
Mapping Spaces in Algebraic Topology 2018(Aug. 30)
Author:Keiichi Sakai


The space of short ropes and the classifying space of the space of long knots
The 59th Cascade Topology Seminar 2017(Oct. 21)
Author:Keiichi Sakai


Lin-Wang type formula for Haefliger's invariant
ICM2014 Satellite Conference on Algebraic Topology 2014(Aug. 11)
Author:Keiichi Sakai


Deloopings of the spaces of long embeddings
International Conference on Topology and Geometry 2013 2013(Sep. 05)
Author:Keiichi Sakai


BV-structures on the homology of the framed long knot space
4th East Asian Conference on Algebraic Topology 2011(Dec. 09)
Author:Keiichi Sakai


配置空間積分によるHaefliger不変量の表示
日本数学会2009年度秋季総合分科会 2009(Sep. 25)
Author:Keiichi Sakai


Non-trivalent graph cocycle and the cohomology of the long knot space
日本数学会2008年度秋季総合分科会 2008(Sep. 24)
Author:Keiichi Sakai


Poisson structure on the homology of the space of framed embeddings
第54回トポロジーシンポジウム 2007(Aug. 07)
Author:Keiichi Sakai


On the space of all embeddings R^1 ->R^n and loop spaces of configuration spaces
Intelligence of Low Dimensional Topology 2005 2005(Nov. 07)
Author:Keiichi Sakai

Research Grants
Grants‐in‐aid for Scientific Research(Research Representative)
平成25年度 - 平成27年度 , 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 , 若手(B)
平成23年度 - 平成24年度 , 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 , 研究活動スタート支援
平成22年度 - 平成22年度 , 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 , 特別研究員奨励費
平成21年度 - 平成21年度 , 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 , 若手研究(B)
2016 - 2019 , 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 , 基盤研究(C)

Social Activities

Social Activitie
Organization of Conferences and/or Symposia
9/7 - 9/10 , Braids, Configuration Spaces and Quantum Topology (2015) , Scientific Committee, Organizing Committee