论文标题
SFT中的Contact Instantons和Pseudoholomoprhic曲线的粘合理论
Gluing theories of contact instantons and of pseudoholomoprhic curves in SFT
论文作者
论文摘要
我们在开放字符串的背景下以及在封闭的字符串\ emph {带有消失的电荷}的背景下发展了接触激体的粘合理论，例如在符号上下文中。这是研究（实际上）平滑模量空间的关键成分之一，即构建联系Instanton Floer共同体所需的（边界）contact Instantons，并且更一般地构建了福卡亚式型Legendrian Submanifolds类别中的filedendrian Submanifolds类别中的触点歧管$（M，ξ）$。作为应用程序，我们应用胶合定理来构建（圆柱形）Legendrian Contact instanton同源性，该构建进入了我们对桑顿（Sandon）问题的解决方案。我们还将这种粘合理论应用于在象征性场理论（SFT）中产生的模量空间，这是通过将前者提升到后者的模量。
We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the study of (virtually) smooth moduli space of (bordered) contact instantons needed for the construction of contact instanton Floer cohomology and more generally for the construction of Fukaya-type category of Legendrian submanifolds in contact manifold $(M,ξ)$. As an application, we apply the gluing theorem to give the construction of (cylindrical) Legendrian contact instanton homology that enters in our solution to Sandon's question for the nondegenerate case. We also apply this gluing theory to that of moduli spaces of holomorphic buildings arising in Symplectic Field Theory (SFT) by canonically lifting the former to that of the latter.
