One way to obtain invariants of some Legendrian submanifolds in 1-jet spaces
J1M, equipped with the standard contact structure, is through the Morse
theoretic technique of generating families. This paper extends the invariant of
generating family cohomology by giving it a product μ2. To define the
product, moduli spaces of flow trees are constructed and shown to have the
structure of a smooth manifold with corners. These spaces consist of
intersecting half-infinite gradient trajectories of functions whose critical
points correspond to Reeb chords of the Legendrian. This paper lays the
foundation for an A∞ algebra which will show, in particular, that
μ2 is associative and thus gives generating family cohomology a ring
structure.Comment: 50 pages, 4 figures, minor change