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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).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
111-143
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Waseda Institute for Advanced Study 1-6-1, Nishi Waseda, Shinjuku-ku, Tokyo 169-8050, Japan
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-5