论文标题
Chekanov-Eliashberg代数的过滤概括
A filtered generalization of the Chekanov-Eliashberg algebra
论文作者
论文摘要
我们定义了与$ \ mathbb {r} _ {t} \ times w $的触点歧管的Legendrian submanifold $λ$相关的新代数，称为平面图代数，并表示为$ pda（λ，\ natecal {p}）$。它是一种非交通性的，过滤的，差异的分级代数，其过滤后的稳定的驯服同构类别是$λ$的不变性，以及其连接组件的分区$ \ Mathcal {p} $。连接$λ$时，$ PDA $是Chekanov-Eliashberg代数。通常，$ pda $差分计数的圆盘磁盘具有多个正面穿刺的圆盘磁盘，使用受字符串拓扑启发的组合框架。
We define a new algebra associated to a Legendrian submanifold $Λ$ of a contact manifold of the form $\mathbb{R}_{t} \times W$, called the planar diagram algebra and denoted $PDA(Λ, \mathcal{P})$. It is a non-commutative, filtered, differential graded algebra whose filtered stable tame isomorphism class is an invariant of $Λ$ together with a partition $\mathcal{P}$ of its connected components. When $Λ$ is connected, $PDA$ is the Chekanov-Eliashberg algebra. In general, the $PDA$ differential counts holomorphic disks with multiple positive punctures using a combinatorial framework inspired by string topology.
