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A RECURSIVE FORMULA FOR THE KHOVANOV COHOMOLOGY OF KANENOBU KNOTS
Lei, Fengchun,Zhang, Meili Korean Mathematical Society 2017 대한수학회보 Vol.54 No.1
Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.
A recursive formula for the Khovanov cohomology of Kanenobu knots
Fengchun Lei,Meili Zhang 대한수학회 2017 대한수학회보 Vol.54 No.1
Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots $K(p,q)$, where $p$ and $q$ are integers. The result implies that the rank of the Khovanov cohomology of $K(p,q)$ is an invariant of $p+q$. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.
LOWER BOUNDS FOR THE NUMBER OF POSITIVE AND NEGATIVE CROSSINGS IN ORIENTED LINK DIAGRAMS
Lei, Fengchun,Zhang, Kai Korean Mathematical Society 2017 대한수학회보 Vol.54 No.6
In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.
Lower bounds for the number of positive and negative crossings in oriented link diagrams
Fengchun Lei,Kai Zhang 대한수학회 2017 대한수학회보 Vol.54 No.6
In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.
A LOWER BOUND FOR THE GENUS OF SELF-AMALGAMATION OF HEEGAARD SPLITTINGS
Li, Fengling,Lei, Fengchun Korean Mathematical Society 2011 대한수학회보 Vol.48 No.1
Let M be a compact orientable closed 3-manifold, and F a non-separating incompressible closed surface in M. Let M' = M - ${\eta}(F)$, where ${\eta}(F)$ is an open regular neighborhood of F in M. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting $V'\;{\cup}_{S'}\;W'$ of M' under some conditions on the distance of the Heegaard splitting.
A lower bound for the genus of self-amalgamation of Heegaard splittings
Fengling Li,Fengchun Lei 대한수학회 2011 대한수학회보 Vol.48 No.1
Let M be a compact orientable closed 3-manifold, and F a non-separating incompressible closed surface in M. Let M'=M-ŋ(F), where ŋ(F) is an open regular neighborhood of F in M. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting V'∪_S'W' of M' under some conditions on the distance of the Heegaard splitting.