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Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces

Research output: Contribution to journalArticle

Yanki Lekili, Alexander Polishchuk

Original languageEnglish
Pages (from-to)273-315
Number of pages43
Early online date30 Nov 2018
Accepted/In press20 Jul 2018
E-pub ahead of print30 Nov 2018
Published5 Feb 2019


King's Authors


We show that all strongly non-degenerate trigonometric solutions of the associative Yang–Baxter equation (AYBE) can be obtained from triple Massey products in the Fukaya categories of square-tiled surfaces. Along the way, we give a classification result for cyclic -algebra structures on a certain Frobenius algebra associated with a pair of 1-spherical objects in terms of the equivalence classes of the corresponding solutions of the AYBE. As an application, combining our results with homological mirror symmetry for punctured tori (cf. [17]), we prove that any two simple vector bundles on a cycle of projective lines are related by a sequence of 1-spherical twists and their inverses.

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