Remarks on symplectic circle actions, torsion and loops

Atallah, Marcelo S

doi:10.2140/agt.2024.24.2367

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Remarks on symplectic circle actions, torsion and loops

Marcelo S Atallah

Algebraic & Geometric Topology 24 (2024) 2367–2384

DOI: 10.2140/agt.2024.24.2367

Abstract

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.

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

Mathematical Subject Classification

Primary: 53D22, 53D40, 57R17

Secondary: 57S15, 57S17

References

Publication

Received: 20 December 2022

Revised: 14 May 2023

Accepted: 28 May 2023

Published: 16 July 2024

Authors

Marcelo S Atallah
Department of Mathematics and Statistics University of Montreal Montreal QC Canada

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 4 (2024)