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CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL

MIKHAIL KHOVANOV

Department of Mathematics, University of California, Davis, CA 95616, USA

https://doi.org/10.1142/S0218216505003750Cited by:61 (Source: Crossref)

Abstract

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 , 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.

Keywords:

AMSC: 57M27

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