A reconstruction theorem for genus zero Gromov-Witten invariants of stacks

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We generalize the First Reconstruction Theorem of Kontsevich and Manin in two respects. First, we allow the target space to be a Deligne-Mumford stack. Second, under some convergence assumptions, we show it suffices to check the hypothesis of $H^2$-generation not on the cohomology ring, but on an any quantum ring in the family given by small quantum cohomology.
Updated to match version published in American Journal of Mathematics, 2007. Only slight modifications

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