Symplectic 4-manifolds with fixed point free circle actions

2012/06/03 by Bowden, Jonathan
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1206.0458

Abstract

We show that recent results of Friedl-Vidussi and Chen imply that a symplectic manifold admits a fixed point free circle action if and only if it admits a symplectic circle action and we give a complete description of the symplectic cone in this case. This then completes the characterisation of symplectic 4-manifolds that admit non-trivial circle actions.

Related

• Symplectic 4-manifolds with a free circle action
• Non-symplectic smooth circle actions on symplectic manifolds
• Classification of symplectic non-Hamiltonian circle actions on 4-manifolds
• Smooth versus symplectic circle actions
• Seiberg-Witten vanishing theorem for S¹-manifolds with fixed points