A note on coherent orientations for exact Lagrangian cobordisms
A note on coherent orientations for exact Lagrangian cobordisms
复制标题
关于精确拉格朗日配边的相干方向的注释
DOI：
10.4171/qt/132
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发表时间：
2017
期刊：
影响因子：
1.1
通讯作者：
Cecilia Karlsson
中科院分区：
文献类型：
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作者：
Cecilia Karlsson
设$L \subset \mathbb R \times J^1（M）$是光滑流形$M$的1-jet空间的辛化中的自旋精确拉格朗日配边。假设$L$具有圆柱勒让德端点$\Lambda_\pm \子集J^1（M）$。众所周知，$\Lambda_\pm$的勒让德接触同调可以通过在$M$的余切丛中伪全纯圆盘的有符号计数来定义。我们还知道，这个计数可以提升到辛化$\mathbb R \times J^1（M）$中伪全纯圆盘的模2计数，并且$L$以函子的方式在$\Lambda_\pm$的$\mathbb Z_2$值DGA：s之间引入态射。我们证明，这与整数系数，以及持有。的证明是建立在定向的模空间的伪全纯磁盘使用封盖运营商在Reeb弦的技术。我们给出了一个表达式，如果我们改变上限运算符，DGA：s将如何改变。
Let $L \subset \mathbb R \times J^1(M)$ be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold $M$. Assume that $L$ has cylindrical Legendrian ends $\Lambda_\pm \subset J^1(M)$. It is well known that the Legendrian contact homology of $\Lambda_\pm$ can be defined with integer coefficients, via a signed count of pseudo-holomorphic disks in the cotangent bundle of $M$. It is also known that this count can be lifted to a mod 2 count of pseudo-holomorphic disks in the symplectization $\mathbb R \times J^1(M)$, and that $L$ induces a morphism between the $\mathbb Z_2$-valued DGA:s of the ends $\Lambda_\pm$ in a functorial way. We prove that this hold with integer coefficients as well. The proofs are built on the technique of orienting the moduli spaces of pseudo-holomorphic disks using capping operators at the Reeb chords. We give an expression for how the DGA:s change if we change the capping operators.
DOI：
10.2140/gt.2023.27.2049
发表时间：
2017-01
期刊：
Geometry & Topology
影响因子：
--
作者：
T. Ekholm;Yankı Lekili
通讯作者：
T. Ekholm;Yankı Lekili