13 citations · 62 across the 13 of their papers we have counts for
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math.GT2011★ 5 cited
On a move reducing the genus of a knot diagram
Kenji Daikoku, Keiichi Sakai, Masamichi Takase
For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this…
math.GT2011★ 3 cited
BV-structures on the homology of the framed long knot space
Keiichi Sakai
We introduce BV-algebra structures on the homology of the space of framed long knots in in two ways. The first one is given in a similar fashion to Chas-Sullivan's s…
math.GT2011★ 6 cited
An integral expression of the first non-trivial one-cocycle of the space of long knots in R^3
Keiichi Sakai
Our main object of study is a certain degree-one cohomology class of the space K of long knots in R^3. We describe this class in terms of graphs and configuration space integrals,…