A Khovanov type link homology with geometric interpretation

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.