A cohomology theory for colored tangles

Carmen Caprau. "A cohomology theory for colored tangles." Banach Center Publications 100.1 (2014): 13-25. <http://eudml.org/doc/282439>.

@article{CarmenCaprau2014,
abstract = {We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of $U_q(sl(2))$. 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.},
author = {Carmen Caprau},
journal = {Banach Center Publications},
keywords = {Khovanov homology; categorification; colored Jones polynomial; foams; webs},
language = {eng},
number = {1},
pages = {13-25},
title = {A cohomology theory for colored tangles},
url = {http://eudml.org/doc/282439},
volume = {100},
year = {2014},
}

TY - JOUR
AU - Carmen Caprau
TI - A cohomology theory for colored tangles
JO - Banach Center Publications
PY - 2014
VL - 100
IS - 1
SP - 13
EP - 25
AB - We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of $U_q(sl(2))$. 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.
LA - eng
KW - Khovanov homology; categorification; colored Jones polynomial; foams; webs
UR - http://eudml.org/doc/282439
ER -