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A Product Structure on Generating Family Cohomology for Legendrian Submanifolds
by
Ziva Myer
Bryn Mawr College, Duke University
In contact geometry, invariants of Legendrian knots in R3, and more generally, Legendrian submanifolds in 1-jet spaces, have been obtained through a variety of techniques. I will discuss how I am extending one such invariant, Generating Family Cohomology, by constructing a product structure. The construction uses moduli spaces of Morse flow trees spaces of intersecting gradient trajectories of functions whose critical points encode Reeb chords of the Legendrian submanifold. This product lays the foundation for an A-infinity algebra that will show, in particular, that Generating Family Cohomology has an invariant ring structure.
Date received: April 10, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbof-06.