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 $M$. We prove that this count can be lifted to a signed count of pseudo-holomorphic disks in $\mathbb{R} \times J^1(M)$, and then we use this to prove that $L$ induces a morphism between the $\mathbb{Z}$-valued DGA:s of the ends, in a functorial way. These results have been indicated in several papers before, our aim is to give rigorous proofs of these facts. 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. 查看全文>>