Plumber’s Algebra Structure on Symplectic Cohomology

I will introduce a new structure on (relative) Symplectic Cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition that ensures the existence of positive Floer data on the surfaces. This action is defined on the chain-level and generalizes the work of Abouzaid–Groman–Varolgunes. I will discuss the relationship of this structure to cohomological field theories, with potential applications to curve counts, as well as algebraic structures defined on variants of Symplectic Cohomology such as Rabinowitz Floer Cohomology.