Massey and Fukaya products on elliptic curves
Alexander Polishchuk
TL;DR
This paper compares Massey and Fukaya products on elliptic curves, recovering classical identities and exploring cases where Massey products are not well-defined, advancing understanding in categorical mirror symmetry.
Contribution
It provides a detailed comparison between Massey and Fukaya products on elliptic curves, including new computations and clarifications of their relationships.
Findings
Recovered Kronecker's classical identity
Computed Fukaya products with undefined Massey counterparts
Enhanced understanding of categorical mirror symmetry
Abstract
This note is a continuation of our paper with E. Zaslow "Categorical mirror symmetry: the elliptic curve", math.AG/9801119. We compare some triple Massey products on elliptic curve with the corresponding Fukaya products on the symplectic torus and recover the classical identity due to Kronecker. We also compute some triple Fukaya products such that the corresponding Massey products are not correctly defined.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models