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Categorifications of the colored Jones polynomial

Mikhail Khovanov
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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 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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Mikhail Khovanov. 2003-02-06. Categorifications of the colored Jones polynomial. https://arxiv.org/abs/math/0302060

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