A Product Structure on Generating Family Cohomology for Legendrian Submanifolds
Doctor of Philosophy (PhD)
One way to obtain invariants of some Legendrian submanifolds in the standard contact manifolds of 1-jet spaces, J1M, is through the Morse theoretic technique of generating families. This dissertation extends the elective but not complete invariant of generating family cohomology by giving it a product μ2. To define the product, moduli spaces of gradient flow trees are constructed and shown to live as the 0-stratum of a compact smooth manifold with corners. These spaces consist of intersecting gradient trajectories of functions whose critical points correspond to Reeb chords of the Legendrian. This dissertation lays the foundation for an A1 algebra which will show, in particular, that μ2 is associative and thus gives generating family cohomology a ring structure.
Myer, Ziva. "A Product Structure on Generating Family Cohomology for Legendrian Submanifolds." PhD diss., Bryn Mawr College, 2017.