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A cohomology theory for colored tangles

100%

Caprau C.

Banach Center Publications

2014

tom 100

nr 1

13-25

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.

Ograniczanie wyników

1 Banach Center Publications

1 Caprau C.

1 2014

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A cohomology theory for colored tangles