Categorifications of the colored Jones polynomial

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.