Chern-Simons gauge theory on a three-manifold M bears an intimate physical relationship to both the open and the closed Gromov-Witten theories. One surprising aspect of this relationship is that the latter theories are cohomological in character, whereas a corresponding cohomological description of Chern-Simons theory is not generally known (nor expected). Nevertheless, as I will explain, in the case that M admits a locally-free U(1) action, some observables in Chern-Simons theory do admit a cohomological description on the moduli space of flat connections on M.

Lecture #12382

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