Remarks on the categorification of colored Jones polynomials

We introduce colored Jones polynomials of nanowords and their categorification. We also prove the existence of a Khovanov-type bicomplex which has three grades.Comment: For Section 2, the author noticed that we did not have a bicomplex that yields a new link invariant yet in this manuscript. Thus, it should be withdraw

Khovanov homology and words

This paper is concerned with nanowords, a generalization of links, introduced by Turaev. It is shown that the system of bigraded homology groups is an invariant of nanowords by introducing a new notion. This paper gives two examples which show the independence of this invariant from some of Turaev's homotopy invariants.Comment: 39 pages; 2 figur