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$S^1$-equivariant relative symplectic cohomology and relative symplectic capacities (2410.01977v2)
Published 2 Oct 2024 in math.SG
Abstract: In this paper, we construct an $S1$-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, we construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative symplectic capacities can detect the diplaceability and the heaviness of a compact subset of a symplectic manifold. We compare the first relative Gutt-Hutchings capacity and the relative symplectic (co)homology capacity and prove that they are equal to each other under a convexity assumption.