Abstract:

In this talk, based on a joint work with Jeongmin Shon, we discuss Reeb dynamics on prequantization circle bundles and the filtered (equivariant) symplectic homology of prequantization line bundles, aka negative line bundles, with symplectically aspherical base. We define (equivariant) symplectic capacities, prove an upper bound on their growth and uniform instability of the filtered symplectic homology, and touch upon the question of stable displacement. We also introduce a new algebraic structure on the positive (equivariant) symplectic homology capturing the free homotopy class of a closed Reeb orbit – the linking number filtration – and use it to give a new proof of the nondegenerate case of the contact Conley conjecture (i.e., the existence of infinitely many simple closed Reeb orbits), not relying on contact homology.