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Geometry and Topology Seminar

Friday, April 28, 2023
4:00pm to 5:00pm
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Linde Hall 187
Colored sl(N) homology and SU(N) representations
Joshua Wang, Department of Mathematics, Harvard University,

The Khovanov homology of a rational knot or link happens to coincide with the cohomology of its space of SU(2) representations that send meridians to traceless matrices. This coincidence is closely related to the spectral sequence from Khovanov homology to an SU(2) instanton homology defined by Kronheimer and Mrowka. Motivated by a conjectural spectral sequence from colored sl(N) homology to a hypothetical colored SU(N) instanton homology, I'll explain how the colored sl(N) homology of the trefoil agrees with the cohomology of its space of SU(N) representations that send meridians to a conjugacy class associated to the color. This gives the first computation of colored sl(N) homology of a nontrivial knot.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit