The Quantum $A_{\infty }$-Relations on the Elliptic Curve

Abstract

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 Getzler and Kapranov. Following Barannikov, these relations may be viewed as defining a solution to the quantum master equation of Batalin-Vilkovisky geometry.

43 pages

References in corpus (2)

• Modular operads and Batalin-Vilkovisky geometry
• The Gromov-Witten potential associated to a TCFT

Cited by in corpus (1)

• Mirror symmetry for the Tate curve via tropical and log corals