2023 Theses Doctoral

A Coproduct Structure on Symplectic Cohomology

Kenigsberg, Lea

Symplectic cohomology is an algebraic invariant which encodes dynamical information of Liouville manifolds; that is, open symplectic manifolds satisfying certain convexity conditions at infinity. In this work we define and investigate a new algebraic structure on symplectic cohomology, the coproduct. To exhibit the non triviality of this structure we study it in the case of complements of smooth divisors. Under certain technical conditions, the symplectic cohomology of such manifolds is particularly amenable to computations via a Morse-Bott model. We define the Morse-Bott coproduct and use it to illustrate that the coproduct structure on the symplectic cohomology of the cotangent bundle of a 3 sphere is not trivial.