The Quantum A_∞-Relations on the Elliptic Curve

2017/11/21 by Michael A. Slawinski, Slawinski, Michael
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1711.07940

Abstract

We define and prove the existence of the Quantum A_∞-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.

Related

• Quantum Elliptic Curves I: Algebraic Case
• Conformal field theory and integrable systems associated with elliptic curves
• Vacuum curves of elliptic L-operators and representations of Sklyanin algebra
• Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve
• Elliptic Calogero-Moser system, crossed and folded instantons, and bilinear identities