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.

152 pages, lots of figures. The main changes from previous versions are made in Sections 1.1, 2.3, 3.2.A, 3.4.C, 3.4.E, 4.2 and 6.2. Two new sections 8 and 9 added to include derivations of explicit signs when $n>1$. Comments are welcome!