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A cohomology theory for colored tangles

Carmen Caprau — 2014

Banach Center Publications

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 ( s l ( 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...

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