Keiichi Sakai

Span of the Jones polynomials of certain v-adequate virtual links 

Journal of Knot Theory and Its Ramifications, Jan, 2021  Peer-reviewed

Generalized connected sum formula for the Arnold invariants of generic plane curves 

TOPOLOGY AND ITS APPLICATIONS, 255 86-108, Mar 15, 2019  Peer-reviewed

The space of short ropes and the classifying space of the space of long knots 

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 18(5) 2859-2873, 2018  Peer-reviewed

BV-structures on the homology of the framed long knot space 

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 11(3) 425-441, Sep, 2016  Peer-reviewed

LIN-WANG TYPE FORMULA FOR THE HAEFLIGER INVARIANT 

HOMOLOGY HOMOTOPY AND APPLICATIONS, 17(2) 317-341, 2015  Peer-reviewed

Deloopings of the spaces of long embeddings 

FUNDAMENTA MATHEMATICAE, 227(1) 27-34, 2014  Peer-reviewed

1-loop graphs and configuration space integral for embedding spaces 

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 152 497-533, May, 2012  Peer-reviewed

On a Move Reducing the Genus of a Knot Diagram 

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 61(3) 1111-1127, 2012  Peer-reviewed

AN INTEGRAL EXPRESSION OF THE FIRST NONTRIVIAL ONE-COCYCLE OF THE SPACE OF LONG KNOTS IN R-3 

PACIFIC JOURNAL OF MATHEMATICS, 250(2) 407-419, Apr, 2011  Peer-reviewed

CONFIGURATION SPACE INTEGRALS FOR EMBEDDING SPACES AND THE HAEFLIGER INVARIANT 

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 19(12) 1597-1644, Dec, 2010  Peer-reviewed

Nontrivalent graph cocycle and cohomology of the long knot space 

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 8(3) 1499-1522, 2008  Peer-reviewed