论文标题
$ a _ {\ infty} $的映射托里 - 自动等同和legendrian升降机的循环联系人
Mapping tori of $A_{\infty}$-autoequivalences and Legendrian lifts of exact Lagrangians in circular contactizations
论文作者
论文摘要
我们研究Quasi Autoequerences $τ的映射Tori $τ：\ Mathcal {a} \ to \ Mathcal {a} $，在对象上引起$ \ Mathbf {z} $的免费动作。更确切地说，当严格且在homset上行动时，或者是指向$ a _ {\ infty} $ - 类别$ \ Mathcal {a} $时，我们计算$τ$的映射曲面，并有一个bimodule Map $ \ nathcal $ \ nathcal {a} a}（ - - ， - - ， - ， - ， - ， - ）{a} - 一些假设。然后，我们应用这些结果，以将福卡亚$ a _ {\ infty} $链接在一起，这是一个精确的Lagrangians家族的类别，以及Chekanov-Eliashberg DG类别的Legendrian Lifts的DG类别。
We study mapping tori of quasi-autoequivalences $τ: \mathcal{A} \to \mathcal{A}$ which induce a free action of $\mathbf{Z}$ on objects. More precisely, we compute the mapping torus of $τ$ when it is strict and acts bijectively on hom-sets, or when the $A_{\infty}$-category $\mathcal{A}$ is directed and there is a bimodule map $\mathcal{A} (-, -) \to \mathcal{A} (-, τ(-))$ satisfying some hypotheses. Then we apply these results in order to link together the Fukaya $A_{\infty}$-category of a family of exact Lagrangians, and the Chekanov-Eliashberg DG-category of Legendrian lifts in the circular contactization.
