638 research outputs found
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
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