Exotic symplectomorphisms and contact circle action
Exotic symplectomorphisms and contact circle action
´Ü´Ç´Ç³¾Ìý±ô¾±²Ô°ì:
Alternate Zoom link:
An exotic symplectomorphism is a symplectomorphism that is not isotopic to the identity through compactly supported symplectomorphisms.Using Floer-theoreticÌýmethods, we prove that the non-existence of an exotic symplectomorphism on the standardÌýsymplecticÌýball, $\mathbb{B}^{2n},$ implies a rather strict topological conditionÌýon 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 itsÌýboundary. Applications include results on theÌýsymplecticÌýmapping class group, the fundamental group of the group of contactomorphisms, and exotic contact structures onÌý$\mathbb{S}^3.$ The talk is based on joint work with Dusan Drobnjak.
Ìý