A colored Khovanov bicomplex

• Autorzy: Noboru Ito
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 103
• Numer: 1
• Strony: 111-143

Daty

wydano

2014

Twórcy

autor

Noboru Ito

• Waseda Institute for Advanced Study 1-6-1, Nishi Waseda, Shinjuku-ku, Tokyo 169-8050, Japan

Identyfikatory

DOI

10.4064/bc103-0-5