A sheaf-theoretic SL(2, C) Floer homology for knots

A sheaf-theoretic SL(2, C) Floer homology for knots

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Laurent Côté, Stanford
Fine Hall 224

I'll outline the construction of an invariant for knots in homology 3-spheres which can be thought of as an SL(2,C) analog of Kronheimer and Mrowka's singular knot instanton homology. This invariant is similar to an invariant of 3-manifolds introduced earlier by Abouzaid and Manolescu, using tools from derived algebraic geometry. I'll therefore begin by summarizing their work and explaining the modifications needed to build this knot invariant. I will then outline some computations of the invariant for various families of knots, and discuss some of its (partly conjectural) properties.  This talk is based entirely on joint work with Ciprian Manolescu.