Colored sl(N) homology and SU(N) representations

Joshua Wang

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arXiv · 2211.08409

Colored sl(N) homology and SU(N) representations

Joshua Wang

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Abstract

We provide the first complete computations of colored sl(N) homology for a nontrivial knot. In doing so, we show that the colored sl(N) homology of the trefoil labeled by an exterior power of the defining representation is isomorphic to the cohomology of a closed manifold naturally associated to the trefoil. This manifold is the set of homomorphisms from the fundamental group of the complement of the trefoil to SU(N) that send meridians to a particular conjugacy class depending on the label. We also provide complete computations and analogous isomorphisms for the first nontrivial link, the Hopf link.

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Joshua Wang. 2022-11-15. Colored sl(N) homology and SU(N) representations. https://arxiv.org/abs/2211.08409

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