论文标题
福卡亚类别的集群类别
Cluster categories from Fukaya categories
论文作者
论文摘要
我们表明，派生包装的Fukaya类别$ d^π\ MATHCAL {w}（x_ {q}^{d+1}）$，派生的紧凑型福卡亚（Fukaya）类别$ d^π\ Mathcal {f} $ x_ {q}^{d+1} $形成calabi - yau三重。结果，商类别$ d^π\ mathcal {w}（x_ {q}^{d+1}）/d^π\ Mathcal {f}（x_ {q}^^{d+1}）$成为与$ q $相关的群集。它的特性之一是calabi-yau结构。还知道，由于Ganatra-Gao-gao-venkatesh的工作，该商类别与Rabinowitz Fukaya类别的准等效类别。我们计算$ l_ {q} $的形态空间中的$ d^π\ Mathcal {w}（x_ {q}^{d+1}）/d^π\ Mathcal {f}（x__ {q} {q}^{d+1}）$使用calabi-yyau结构，floo cohom of rabin cohom of ravit $ l_ {q} $。
We show that the derived wrapped Fukaya category $D^π\mathcal{W}(X_{Q}^{d+1})$, the derived compact Fukaya category $D^π\mathcal{F}(X_{Q}^{d+1})$ and the cocore disks $L_{Q}$ of the plumbing space $X_{Q}^{d+1}$ form a Calabi--Yau triple. As a consequence, the quotient category $D^π\mathcal{W}(X_{Q}^{d+1})/D^π\mathcal{F}(X_{Q}^{d+1})$ becomes the cluster category associated to $Q$. One of its properties is a Calabi--Yau structure. Also it is known that this quotient category is quasi-equivalent to the Rabinowitz Fukaya category due to the work of Ganatra--Gao--Venkatesh. We compute the morphism space of $L_{Q}$ in $D^π\mathcal{W}(X_{Q}^{d+1})/D^π\mathcal{F}(X_{Q}^{d+1})$ using the Calabi--Yau structure, which is isomorphic to the Rabinowitz Floer cohomology of $L_{Q}$.
