Séminaires : Séminaire d'Analyse et Géométrie

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I will explain how the local real GW theory of curves gives rise to a 2-dimensional Klein TQFT defined on an extension of the category of unorientable surfaces. We use this structure to completely solve the theory by providing a closed formula for the local real GW invariants in terms of representation theoretic data. As a corollary we obtain the local version of the real Gopakumar-Vafa formula. In the case of the resolved conifold the partition function of the real GW invariants agrees with that of the SO/Sp Chern-Simons theory on \(S^3\).