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Crossing change on Khovanov homology and a categorified Vassiliev skein relation
Noboru Ito, Jun Yoshida
Khovanov homology is a categorification of the Jones polynomial, so it may be seen as a kind of quantum invariant of knots and links. Although polynomial quantum invariants are dee…
Arrow diagrams on spherical curves and computations
Noboru Ito, Masashi Takamura
We give a definition of an integer-valued function derived from arrow diagrams for the ambient isotopy classes of oriented spherical curves. Then, we introduce…
On a Poincaré polynomial from Khovanov homology and Vassiliev invariants
Noboru Ito, Masaya Kameyama
We introduce a Poincaré polynomial with two-variable and for knots, derived from Khovanov homology, where the specialization is a Vassiliev invariant…
Goussarov-Polyak-Viro Conjecture for degree three case
Noboru Ito, Yuka Kotorii, Masashi Takamura
Although it is known that the dimension of the Vassiliev invariants of degree three of long virtual knots is seven, the complete list of seven distinct Gauss diagram formulas have…