Publications of Keiichi Sakai
Published / Accepted papers (linked to MathSciNet)
They can also be found in arXiv.
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(with Minori Okamura)
Span of the Jones polynomials of certain v-adequate virtual links,
Journal of Knot Theory and Its Ramifications,
volume 30, No. 01 (2021),
2150001
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(with Ryutaro Sugiyama)
Generalized connected sum formula for the Arnold invariants of generic plane curves,
Topology and its Applications,
volume 255 (2019),
pages 86-108
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(with Syunji Moriya)
The space of short ropes and the classifying space of the space of long knots,
Algebraic and Geometric Topology
18-5 (2018),
pages 2859-2873
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Lin-Wang type formula for the Haefliger invariant,
Homology, Homotopy and Applications,
Volume 17 (2015),
Number 2,
pages 317-341
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BV-structures on the homology of the framed long knot space,
Journal of Homotopy and Related Structures,
Volume 11 (2016), issue 3,
pages 425-441
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Deloopings of the spaces of long embeddings,
Fundamenta Mathematicae,
Volume 227 (2014),
Number 1,
pages 27-34
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(with Kenji Daikoku and Masamichi Takase)
On a move reducing the genus of a knot diagram,
Indiana University Mathematics Journal,
Volume 61 (2012), issue 3,
pages 1111-1127
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(with Tadayuki Watanabe)
1-loop graphs and configuration space integral for embedding spaces,
Mathematical Proceedings of the Cambridge Philosophical Society,
Volume 152, Issue 03 (May 2012),
pages 497-533
Shinshu U Institutional Repository
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An integral expression of the first non-trivial one-cocycle of the space of long knots in R3,
Pacific Journal of Mathematics,
Volume 250 (2011), No. 2,
pages 407-419
Shinshu U Institutional Repository
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Configuration space integrals for embedding spaces and the Haefliger invariant,
Journal of Knot Theory and Its Ramifications,
Volume 19, (2010) No. 12,
pages 1597-1644
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Nontrivalent graph cocycle and the cohomology of long knot space,
Algebraic and Geometric Topology
8:3 (2008),
pages 1499-1522
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Poisson structures on the homology of the space of knots,
Geometry and Topology Monographs,
Volume 13 (2008),
Groups, homotopy and configuration spaces (Tokyo 2005),
pages 463-482
Expositions
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Embedding spaces, configuration spaces and Vassiliev invariants (in Japanese),
uwv(Sugaku) volume 72, pages 285-336,
The Mathematical Society of Japan
Preprints / In preparation
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(with Saki Kanou) The Fox-Hatcher cycle and a Vassiliev invariant of order three,
arXiv.2203.15329
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Bott-Taubes construction for the space of framed long knots, preprint
Errata
Sorry for misspelling the name of Thistleswaite in JKTR paper (2021).
AGT paper (2008) and Pacific J Math paper (2011) contain sign errors;
the signs of 7th, 8th and 9th graphs in the non-trivalent graph cocycle should be replaced by respectively +, - and +.
These corrections do not cause any problems on the results of these papers since these graphs do not essentially contribute to the integrals. (3 June 2013)
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