论文标题
包裹的缝合的legendrian同源性和本地2编的单位
Wrapped sutured Legendrian homology and unit conormal of local 2-braids
论文作者
论文摘要
我们将缝合的框架扩展到具有边界的传奇人物的情况。利用拉格朗日浮子理论中的想法，我们定义了一对缝合的传奇人物的圆柱形和包裹的缝合式传奇同源物。它们将其拟合到一个精确的序列中，精确的三角形沿着固定在边界上的legendrian同位素不变。对于单个Legendrian，我们还定义了其Chekanov-Eliashberg DGA的包装版本。我们的主要示例是通过单元构造结构获得的：Submanifold $ n \ subset M $，因此$ \ partial n \ subset \ partial m $，诱导了缝合的legendrian $λ_n\ subset st^*m $，因此我们得到了具有边界歧管的平滑无花果。作为一个简单的应用程序，我们表明，如果两个局部2编织物的吻合是同位素的（作为具有固定边界的传统人），则辫子是等效的。
We extend the sutured framework to the case of Legendrians with boundary. Using ideas from Lagrangian Floer theory, we define the cylindrical and the wrapped sutured Legendrian homologies of a pair of sutured Legendrians. They fit together into an exact sequence, and the exact triangle is invariant along an Legendrian isotopy fixed at the boundary. For a single Legendrian, we also define a wrapped version of its Chekanov-Eliashberg dga. Our main example of sutured Legendrian is obtained via the unit conormal construction : a submanifold $N \subset M$, such that $\partial N \subset \partial M$ , induces a sutured Legendrian $Λ_N \subset ST^*M$, thus we get smooth invariants of manifolds with boundary. As a simple application, we show that if the conormals of two local 2-braids are isotopic (as Legendrians with fixed boundary), then the braids are equivalent.
