Vafa-Witten invariants of 3-manifolds

3-manifolds and Vafa-Witten theory

We initiate explicit computations of the vafa-witten invariants of 3-manifolds, analogous to floer groups in the context of donaldson theory.In particular, we explicitly compute the vafa-witten invariants of 3-manifolds in a family of concrete examples relevant to various surgery operations (the gluck twist, knotsurgeries, log-transforms).We also describe the structural properties that areexpected to hold for general 3-manifolds, including the modular group action, the relation to floer homology, infinite-dimensionality for an arbitrary 3-manifold, and the absence of instantons.