The quantum \(A_{\infty}\)-relations on the elliptic curve. (English) Zbl 07904731
Summary: We define and prove the existence of the Quantum \(A_{\infty}\)-relations on the Fukaya category of the elliptic curve, using the notion of the Feynman transform of a modular operad, as defined by E. Getzler and M. M. Kapranov [Compos. Math. 110, No. 1, 65–126 (1998; Zbl 0894.18005)]. Following S. Barannikov [Int. Math. Res. Not. 2007, No. 19, Article ID rnm075, 31 p. (2007; Zbl 1135.18006)], these relations may be viewed as defining a solution to the quantum master equation of Batalin-Vilkovisky geometry.
MSC:
| 18N70 | \(\infty\)-operads and higher algebra |
| 18M70 | Algebraic operads, cooperads, and Koszul duality |
| 14H52 | Elliptic curves |
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