Symplectic 4-manifolds with fixed point free circle actions

2012/06/03 by Jonathan Bowden, Bowden, Jonathan
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1206.0458

5 pages (to appear in Proc. Amer. Math. Soc.)

openalex publication_date 2012/06/03 · arxiv created 2013/04/13 · arxiv updated 2013/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant

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