SAKAI, Keiichi | Shinshu University Researcher Directory

Academic Organization	Academic Assembly　School of Science and Technology　Institute of Science	TEL
Education and Research Organization	Faculty of Science　Department of Mathematics	FAX
Position	Professor	Mail Address
Address	3-1-1, Asahi, Matsumoto City 390-8621	Web site	http://math.shinshu-u.ac.jp/~ksakai/index.html

Profile

Research Field: topology

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

Academic Societies: Academic Societies
日本数学会

Research

Books, Articles, etc.: Articles
The Fox-Hatcher cycle and a Vassiliev invariant of order three
Pacific Journal of Mathematics (to appear ) 2023
Author:Saki Kanou, Keiichi Sakai

Span of the Jones polynomials of certain v-adequate virtual links
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS,30(1) 2021(Jan.)
Author:Okamura, Minori; Sakai, Keiichi;
Keywords:Virtual links; (pseudo-)adequacy; the Kauffman-Murasugi-Thislethwaite inequality; Turaev surfaces;

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
The Fox-Hatcher cycle and a Vassiliev invariant of order three
New Developments in Four Dimensions 2022(Jun. 17)
Presenter:Keiichi Sakai

The Fox-Hatcher cycle and a Vassiliev invariant of order three
Differential Topology Seminar 2022(May 17)
Presenter:Keiichi Sakai

Span of the Jones polynomials of certain v-adequate virtual links
Moscow-Beijing topology seminar (online) 2021(Mar. 17)
Presenter:Keiichi Sakai

L-infinity algebras and graph cocycles
Homotopy Theory Symposium 2019(Oct. 28)
Presenter:Keiichi Sakai

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

Lin-Wang type formula for Haefliger's invariant
2014(Aug. 11)
Presenter:Keiichi Sakai

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

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

MISC
Embedding spaces, configuration spaces and Vassiliev invariants
数学,72(3):285 2020(Jul.)
Author:Keiichi Sakai

Research Grants: Grants‐in‐aid for Scientific Research(Research Representative)
2020 - 2025 , 埋め込みのなす空間のトポロジーと有限型不変量 , 基盤(C)
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)
2013 - 2015 , 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)
2011 - 2012 , 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
2010 - 2010 , 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
2009 - 2009 , 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)

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

Shinshu University Researcher Directory

SAKAI Keiichi

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Research

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SAKAI　Keiichi