# A cohomology theory for colored tangles

Banach Center Publications (2014)

- Volume: 100, Issue: 1, page 13-25
- ISSN: 0137-6934

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topCarmen 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 -

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