Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the ...Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.展开更多
The alternating links give a classical class of links.They play an important role in Knot Theory.Ozsvath and Szab6 introduced a quasi-alternating link which is a generalization of an alternating link.In this paper we ...The alternating links give a classical class of links.They play an important role in Knot Theory.Ozsvath and Szab6 introduced a quasi-alternating link which is a generalization of an alternating link.In this paper we review some results of alternating links and quasi-alternating links on the Jones polynomial and the Khovanov homology.Moreover,we introduce a long pass link.Several problems worthy of further study are provided.展开更多
Although computing the Khovanov homology of links is common in literature, no general formulae have been given for all of them. We give the graded Euler characteristic and the Khovanov homology of the 2-strand braid l...Although computing the Khovanov homology of links is common in literature, no general formulae have been given for all of them. We give the graded Euler characteristic and the Khovanov homology of the 2-strand braid link ,, and the 3-strand braid .展开更多
We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric ...We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric complex.The homology has also geometric descriptions by introducing the genus generating operations.We prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology groups.As an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.展开更多
基金The NSF(11271282,11371013)of Chinathe Graduate Innovation Fund of USTS
文摘Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.
文摘The alternating links give a classical class of links.They play an important role in Knot Theory.Ozsvath and Szab6 introduced a quasi-alternating link which is a generalization of an alternating link.In this paper we review some results of alternating links and quasi-alternating links on the Jones polynomial and the Khovanov homology.Moreover,we introduce a long pass link.Several problems worthy of further study are provided.
文摘Although computing the Khovanov homology of links is common in literature, no general formulae have been given for all of them. We give the graded Euler characteristic and the Khovanov homology of the 2-strand braid link ,, and the 3-strand braid .
基金Supported by NSFC(Grant Nos.11329101 and 11431009)
文摘We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric complex.The homology has also geometric descriptions by introducing the genus generating operations.We prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology groups.As an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.
