Compactness of instantons and the Atiyah-Floer conjecture

Abstract: The Atiyah-Floer conjecture says that the instanton Floer homology of a three-manifold (constructed via gauge theory) agrees with a Lagrangian Floer homology (constructed via symplectic geometry) associated to a splitting of the manifold. Atiyah's heuristic argument of this conjecture relies on a compactness result for instantons in a certain adiabatic limit. I will present a proof of such a compact theorem for the case when the gauge group is SO(3), as well as another compactness theorem related to bounding chains on the symplectic side.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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