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arXiv · 1712.00364

A product structure on Generating Family Cohomology for Legendrian Submanifolds

Ziva Myer
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Abstract

One way to obtain invariants of some Legendrian submanifolds in 1-jet spaces $J^1M$, 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 $\mu_2$. 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 $A_\infty$ algebra which will show, in particular, that $\mu_2$ is associative and thus gives generating family cohomology a ring structure.

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Ziva Myer. 2017-11-30. A product structure on Generating Family Cohomology for Legendrian Submanifolds. https://arxiv.org/abs/1712.00364

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