Abstract
Donovan and Wemyss (Duke Math J 165(8):1397–1474, 2016) introduced the contraction algebra of flopping curves in threefold. They conjectured that the contraction algebra determines the formal neighborhood of the underlying singularity of the contraction. In this paper, we prove that the contraction algebra together with its natural $$A_\infty $$ -structure constructed in Hua and Toda (Int Math Res Not rnw333, 2017), determine the formal neighborhood of the singularity.
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