Orientations of Morse flow trees in Legendrian contact homology

Abstract

Let $\Lambda$ be a closed, connected, spin Legendrian submanifold of the 1-jet space of a smooth $n$-dimensional manifold. We give a coherent orientation scheme for the moduli space of rigid Morse flow trees of $\Lambda$, implying that the Legendrian contact homology of $\Lambda$ with integer coefficients can be computed using Morse flow trees. If $n>1$ then this orientation scheme can be computed with an algorithm which uses intersections of oriented flow manifolds in $M$ together with combinatorial data coming from the trees.