Categorifications of the colored Jones polynomial

Details Categorifications of the colored Jones polynomial Categorifications of the colored Jones polynomial

2003-02-06

arxiv.org/abs/math/0302060v1

J. Knot theory and its Ramifications 14 (2005) no.1, 111--130

Mathematics

Quantum Algebra

23 pages, latex, 16 eps figures

Scientific paper

The colored Jones polynomial of links has two natural normalizations: one in which the n-colored unknot evaluates to [n+1], the quantum dimension of the (n+1)-dimensional irreducible representation of quantum sl(2), and the other in which it evaluates to 1. For each normalization we construct a bigraded cohomology theory of links with the colored Jones polynomial as the Euler characteristic.

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