Floer theory of higher rank quiver 3-folds
英文摘要：
We study threefolds $Y$ fibred by $A_m$-surfaces over a curve $S$ of positive genus. An ideal triangulation of $S$ defines, for each rank $m$, a quiver $Q(Δ_m)$, hence a $CY_3$-category $(C,W)$ for any potential $W$ on $Q(Δ_m)$. We show that for $ω$ in an open subset of the Kähler cone, a subcategory of a sign-twisted Fukaya category of $(Y,ω)$ is quasi-isomorphic to $(C,W_{[ω]})$ for a certain generic potential $W_{[ω]}$. This partially establishes a conjecture of Goncharov concerning `categorifications' of cluster varieties of framed $PGL_{m+1}$-local systems on $S$, and gives a symplectic geometric viewpoint on results of Gaiotto, Moore and Neitzke.
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