topology

Polyak-Viro type formula for the Milnor triple linking number of link diagrams with multiple-crossings
Yusaku Okuhara and Keiichi Sakai
31 Mar. 2025

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, Refereed

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, Refereed

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, Refereed

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, Refereed

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

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

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

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, Invited

Gerstenhaber 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, Invited

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

日本数学会

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

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