David Rose (UNC), “gl_n homologies, annular evaluation, and symmetric webs”

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Abstract: A conjecture of Dunfield-Gukov-Rasmussen predicts a family of differentials on reduced HOMFLYPT homology, indexed by the integers, that give rise to a corresponding family of reduced link homologies. We’ll discuss a variant of this conjecture, constructing an unreduced link homology theory categorifying the quantum gl_n link invariant for all non-zero values of n (including negative values!). To do so, we employ the technique of annular evaluation, which uses categorical traces to define and characterize type A link homology theories in terms of simple data assigned to the unknot. Of particular interest is the case of negative n, which gives a categorification of the “symmetric webs” presentation of the type A Reshetikhin-Turaev invariant, and which produces novel categorifications thereof (i.e. distinct from the Khovanov-Rozansky theory).