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# The Fundamental Group of $S^1$-manifolds

Published:2010-07-06
Printed: Oct 2010
• Leonor Godinho,
Departmento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
• M. E. Sousa-Dias,
Departmento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
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## Abstract

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian $S^1$-action. Several examples are presented to illustrate our main results.
 MSC Classifications: 53D20 - Momentum maps; symplectic reduction 37J10 - Symplectic mappings, fixed points 55Q05 - Homotopy groups, general; sets of homotopy classes