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

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Manolescu, Ciprian

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A sheaf-theoretic model for SL(2,C) Floer homology
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19
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I will explain the construction of a new homology theory for three-manifolds, defined using perverse sheaves on the SL(2,C) character variety. Our invariant is a model for an SL(2,C) version of Floer’s instanton homology. I will present a few explicit computations for Brieskorn spheres, and discuss the connection to the Kapustin-Witten equations and Khovanov homology. This is joint work with Mohammed Abouzaid.