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A colored Khovanov bicomplex

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Ito N.

Banach Center Publications

2014

tom 103

nr 1

111-143

In this note, we prove the existence of a tri-graded Khovanov-type bicomplex (Theorem 1.2). The graded Euler characteristic of the total complex associated with this bicomplex is the colored Jones polynomial of a link. The first grading of the bicomplex is a homological one derived from cabling of the link (i.e., replacing a strand of the link by several parallel strands); the second grading is related to the homological grading of ordinary Khovanov homology; finally, the third grading is preserved by the differentials, and corresponds to the degree of the variable in the colored Jones polynomial. In particular, we introduce a way to take a small cabling link diagram directly from a big cabling link diagram (Theorem 3.2).

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1 Banach Center Publications

1 Ito N.

1 2014

Wyniki wyszukiwania

A colored Khovanov bicomplex