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Holomorphic curves in exploded manifolds: compactness. (English) Zbl 1322.32013
Summary: This paper establishes compactness results for the moduli stack of holomorphic curves in suitable exploded manifolds. This together with [B. Parker, “Gromov Witten invariants of exploded manifolds”, Preprint, arXiv:1102.0158] and [B. Parker, “Holomorphic curves in exploded torus fibrations: regularity”, Preprint, arXiv:0902.0087] allows the definition of Gromov-Witten invariants of these exploded manifolds.

32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F60 Teichmüller theory for Riemann surfaces
14H15 Families, moduli of curves (analytic)
32Q60 Almost complex manifolds
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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