摘要
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.
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.
基金
Supported by NSFC(Grant Nos.11329101 and 11431009)
