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Traces, current algebras, and link homologies

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HTLW04 - Quantum topology and categorified representation theory

We'll show how categorical traces and foam categories can be used to define an invariant of braid conjugacy, which can be viewed as a “universal” type-A braid invariant. Applying various functors, we recover several known link homology theories, both for links in the solid torus, and, more-surprisingly, for links in the 3-sphere. Variations on this theme produce new annular invariants, and, conjecturally, a homology theory for links in the 3-sphere which categorifies the sl(n) link polynomial but is distinct from the Khovanov-Rozansky theory. Lurking in the background of this story is a family of current algebra representations.

This is joint work with Queffelec and Sartori.

This talk is part of the Isaac Newton Institute Seminar Series series.

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