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.

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关于精确拉格朗日坐标的相干方向的说明

令 $L \subset \mathbb R \times J^1(M)$ 是光滑流形 $M$ 的 1-jet 空间辛化中的自旋、精确拉格朗日协边。假设 $L$ 具有圆柱形 Legendrian 端 $\Lambda_\pm \subset J^1(M)$。众所周知，$\Lambda_\pm$ 的勒让德接触同调可以用整数系数定义，通过 $M$ 的余切丛中伪全纯圆盘的有符号计数。众所周知，这个计数可以提升到辛化 $\mathbb R \times J^1(M)$ 中伪全纯圆盘的 mod 2 计数，并且 $L$ 在 $\mathbb Z_2$-valued DGA:s 以函数方式结束 $\Lambda_\pm$。我们证明这也适用于整数系数。证明建立在使用 Reeb 和弦上的封盖算子对伪全纯圆盘的模空间进行定向的技术上。如果我们改变上限运算符，我们给出了 DGA:s 如何变化的表达式。