Log Gromov-Witten invariants of Calabi-Yau 3-folds are canonically represented by holomorphic lagrangian cycles in a new Weinstein-style category, with a conjectural unitary bridge to Donaldson-Thomas invariants.
Exploded Manifolds
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abstract
This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov-Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov-Witten invariants.
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Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences
Log Gromov-Witten invariants of Calabi-Yau 3-folds are canonically represented by holomorphic lagrangian cycles in a new Weinstein-style category, with a conjectural unitary bridge to Donaldson-Thomas invariants.