Symplectic homology of displaceable Liouville domains and Leafwise intersection points

Abstract

In this note we prove that the symplectic homology of a Liouville domain W displaceable in the symplectic completion vanishes. Nevertheless if the Euler characteristic of (W,\p W) is odd, the filtered symplectic homologies of W do not vanish and give rise to leafwise intersection points on the symplectic completion of W for a perturbation displacing $W$ from itself. In contrast to the existing results we can find a leafwise intersection point for a given period but its energy varies by period instead.

8 pages, minor changes, to appear in Geom. Ded

References in corpus (3)

• Functors and Computations in Floer homology with Applications Part II
• $S^1$-equivariant symplectic homology and linearized contact homology
• Displaceability and the mean Euler characteristic