论文标题
高级箭袋的浮子理论3倍
Floer theory of higher rank quiver 3-folds
论文作者
论文摘要
我们在曲线$ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ fibred中研究。 $ s $的理想三角剖分定义，对于每个等级$ m $，Quiver $ Q（δ_M）$，因此，$ cy_3 $ -category $（c，w）$（c，w）$ in $ q（Δ_M）$上的任何潜在$ W $。我们表明，对于$ω$，在kähler锥的一个开放子集中，$（y，ω）$的标志性fukaya类别的子类别是Quasi is-Isomorphic，to $（c，w _ {[ω]}）$，对于某些通用的潜在$ w _ {[ω] {[ω]} $。这部分建立了Goncharov的猜想，涉及框架上$ pgl_ {m+1} $的群集品种的“分类” - $ s $上的本地系统，并给出了Gaiotto，Moore，Moore和Neitzke结果的符合性几何观点。
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.
