Quiver algebras as Fukaya categories

Abstract

We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasi-projective 3-folds associated to meromorphic quadratic differentials. Together with previous results, this yields non-trivial computations of spaces of stability conditions on Fukaya categories of symplectic 6-manifolds.

50 pages, 13 figures. Version 3 corrects a sign error, exchanging the roles of the twisted and untwisted Fukaya categories

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• Floer theory of higher rank quiver 3-folds
• Finite presentations for spherical/braid twist groups from decorated marked surfaces