Fundamental group of $\operatorname{Symp}(M,\omega )$ with no circle action

Jarek Kędra

Mathematical Sciences, University of Aberdeen Meston Building, King’s College Aberdeen AB24 3UE, Scotland, UK
Institute of Mathematics, University of Szczecin Wielkopolska 15, 70-451 Szczecin, Poland


Abstract: We show that $\pi _1(\operatorname{Symp}(M, \omega ))$ can be nontrivial for $M$ that does not admit any symplectic circle action.

AMSclassification: primary 57S05; secondary 53C15.

Keywords: symplectomorphism, circle action.