# A colored Khovanov bicomplex

Banach Center Publications (2014)

- Volume: 103, Issue: 1, page 111-143
- ISSN: 0137-6934

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topNoboru Ito. "A colored Khovanov bicomplex." Banach Center Publications 103.1 (2014): 111-143. <http://eudml.org/doc/281994>.

@article{NoboruIto2014,

abstract = {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).},

author = {Noboru Ito},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {111-143},

title = {A colored Khovanov bicomplex},

url = {http://eudml.org/doc/281994},

volume = {103},

year = {2014},

}

TY - JOUR

AU - Noboru Ito

TI - A colored Khovanov bicomplex

JO - Banach Center Publications

PY - 2014

VL - 103

IS - 1

SP - 111

EP - 143

AB - 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).

LA - eng

UR - http://eudml.org/doc/281994

ER -

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