TL;DR
This paper connects quiver-based triangulated categories with Fukaya categories of certain 3-folds, enabling new computations of stability conditions on symplectic 6-manifolds.
Contribution
It introduces an embedding of quiver-derived categories into Fukaya categories of quasi-projective 3-folds, advancing the understanding of their structure and stability conditions.
Findings
Embedded quiver categories into Fukaya categories of 3-folds.
Computed spaces of stability conditions on Fukaya categories.
Extended previous results to symplectic 6-manifolds.
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.
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