论文标题
福卡亚表面，球形对象和映射课程组类别
Fukaya categories of surfaces, spherical objects, and mapping class groups
论文作者
论文摘要
我们证明，属属的封闭表面衍生的福卡亚类别中的每个球形对象至少两个，其Chern特征代表非零的Hochschild同源性类别是与配备有等级的一个本地系统的简单封闭曲线的准同态。 （同源假设是必要的。）这在很大程度上回答了Haiden，Katzarkov和Kontsevich的问题。因此，从福卡亚类别的自动等量组到映射类组有自然的陈述。这些证据吸引并说明了许多最近的发展：包装类别的Quiver代数模型，将福卡亚类别造成隔离，对有限和连续的群体行动的刻度浮动理论以及同源镜像对称性。包括对高维符号映射类组的应用。
We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least two whose Chern character represents a non-zero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a rank one local system. (The homological hypothesis is necessary.) This largely answers a question of Haiden, Katzarkov and Kontsevich. It follows that there is a natural surjection from the autoequivalence group of the Fukaya category to the mapping class group. The proofs appeal to and illustrate numerous recent developments: quiver algebra models for wrapped categories, sheafifying the Fukaya category, equivariant Floer theory for finite and continuous group actions, and homological mirror symmetry. An application to high-dimensional symplectic mapping class groups is included.
