Joint IAS/PU Symplectic Geometry Seminar

Work of Diogo, Diogo-Lisi, and Ganatra-Pomerleano have explored the idea of computing symplectic cohomology of a divisor complement. In particular, we may compute the associated graded of the standard action filtration on symplectic cohomology in terms of the topology of the divisor complement and the topology of the circle bundle associated to the normal bundle of the divisor, and the obstruction to splitting into the associated graded is encoded by genus 0 relative Gromov-Witten type moduli spaces. In this talk, we will explore how to lift this to Floer homotopy theory; here, framed bordism classes of higher-dimensional genus 0 relative Gromov-Witten type moduli spaces obstruct the Floer homotopy type from splitting into its associated graded, where the latter is computed topologically. Time permitting, we will discuss example computations.