论文标题
Lagrangian信函和广义Viterbo限制函数
Lagrangian correspondences and the generalized Viterbo restriction functor
论文作者
论文摘要
我们研究包装福卡亚类别的两种函子：1）viterbo限制性函数用于包含liouville子域； 2）拉格朗日对应函数与副域的包含的图表相关联，称为图对应函子。我们证明，这两个函子在定义了Viterbo限制函数的子类别上一致。我们还将Viterbo限制性函数扩展到了Lagrangian Submanifolds的非严格限制的情况下，该限制使用另一种线性化的Legendrian同源性构建，它产生了包裹的Fukaya类别的自然对象变形。另一方面，图对应函数自然定义在整个包装的福卡亚类别中，这是一个先验的值，以某些拉格朗日沉浸式作为对象的包装福卡亚类别的合适扩大中的值。我们证明了图对应函数与Viterbo限制函数的扩展一致。
We study two kinds of functors of wrapped Fukaya categories: 1) the Viterbo restriction functor for an inclusion of a Liouville sub-domain; 2) the Lagrangian correspondence functor associated to the graph of the completion of the inclusion of the sub-domain, named the graph correspondence functor. We prove that these two functors agree on the sub-category where the Viterbo restriction functor is defined. We also extend the Viterbo restriction functor to the case of non-strongly-exact restrictions of Lagrangian submanifolds, which yields a natural object-wise deformation of the wrapped Fukaya category, constructed using another theory - linearized Legendrian homology. On the other hand, the graph correspondence functor is naturally defined on the whole wrapped Fukaya category, a priori taking values in a suitable enlargement of the wrapped Fukaya category having certain Lagrangian immersions as objects. We prove that the graph correspondence functor agrees with the extension of the Viterbo restriction functor.
