Geodesic
Remarks on symplectic circle actions, torsion and loops
Atallah, Marcelo S1
1 Department of Mathematics and Statistics, University of Montreal, Montreal QC, Canada
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2367-2384

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible. As a consequence, we obtain a new vanishing result for the flux group and new instances where the presence of a fixed point of a symplectic circle action is a sufficient condition for it to be Hamiltonian. We also obtain applications to symplectic torsion; more precisely, nontrivial elements of Symp ⁡ 0(M,ω) that have finite order.

DOI : 10.2140/agt.2024.24.2367
Keywords: symplectic geometry, symplectic topology, differential geometry, dynamical systems, geometric topology, symplectic circle actions, symplectic torsion, finite groups, group actions, Floer–Novikov theory, Morse–Novikov theory, flux

Atallah, Marcelo S 1

1 Department of Mathematics and Statistics, University of Montreal, Montreal QC, Canada 
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Atallah, Marcelo S. Remarks on symplectic circle actions, torsion and loops. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2367-2384. doi: 10.2140/agt.2024.24.2367

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