13 citations · 62 across the 13 of their papers we have counts for
13 papers
The Fox-Hatcher cycle and a Vassiliev invariant of order three
Saki Kanou, Keiichi Sakai
We show that the integration of a 1-cocycle I(X) of the space of long knots in R^3 over the Fox-Hatcher 1-cycles gives rise to a Vassiliev invariant of order exactly three. This re…
Span of the Jones polynomials of certain v-adequate virtual links
Minori Okamura, Keiichi Sakai
It is known that the Kauffman-Murasugi-Thislethwaite type inequality becomes an equality for any (possibly virtual) adequate link diagram. We refine this condition. As an applicati…
Generalized connected sum formula for the Arnold invariants of generic plane curves
Keiichi Sakai, Ryutaro Sugiyama
We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants …
The space of short ropes and the classifying space of the space of long knots
Syunji Moriya, Keiichi Sakai
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category)…
Lin-Wang type formula for the Haefliger invariant
Keiichi Sakai
In this paper we study the Haefliger invariant for long embeddings in terms of the self-intersections of their projections to $\ma…
Deloopings of the spaces of long embeddings
Keiichi Sakai
The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two).…