  Let $\Lambda$ be a Legendrian submanifold of the 1-jet space of a smooth
manifold. Associated to $\Lambda$ there is a Legendrian invariant called
Legendrian contact homology, which is defined by counting rigid
pseudo-holomorphic disks of $\Lambda$. Moreover, there exists a bijective
correspondence between rigid pseudo-holomorphic disks and rigid Morse flow
trees of $\Lambda$, which allows us to compute the Legendrian contact homology
of $\Lambda$ via Morse theory.
  If $\Lambda$ is spin, then the moduli space of the rigid disks can be given a
coherent orientation, so that the Legendrian contact homology of $\Lambda$ can
be defined with coefficients in $\mathbb Z$. In this paper we give an explicit
algorithm for computing the corresponding orientation of the moduli space of
rigid Morse flow trees, using the Morse theoretical framework.

Symplectic Geometry