Exotic symplectomorphisms and contact circle actions

Abstract

Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball, ${\mathbb{B}}^{2n},$ implies a rather strict topological condition on the free contact circle actions on the standard contact sphere, ${\mathbb{S}}^{2n-1}.$ We also prove an analogue for a Liouville domain and contact circle actions on its boundary. Applications include results concerning the symplectic mapping class group and the fundamental group of the group of contactomorphisms.

v2: revision; 31 pages; 3 figures

References in corpus (1)

• The combinatorics of Morse theory with boundary

Cited by in corpus (1)

• Hamiltonian perturbations in contact Floer homology