We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of . We show that the corresponding colored invariants of tangles can be assembled into invariants of bigger tangles. For the case of knots and links, the corresponding theory is a categorification of the colored Jones polynomial, and provides a tool for efficient computations of the resulting colored invariant of knots and links. Our theory is defined over the Gaussian integers ℤ[i] (and more generally over ℤ[i][a,h], where a,h are formal parameters), and enhances the existing categorifications of the colored Jones polynomial.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc100-0-1,
author = {Carmen Caprau},
title = {A cohomology theory for colored tangles},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {13-25},
zbl = {1302.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc100-0-1}
}
Carmen Caprau. A cohomology theory for colored tangles. Banach Center Publications, Tome 102 (2014) pp. 13-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc100-0-1/