The fundamental group of S¹-manifolds

2005/05/19 by Leonor Godinho, L. Godinho, Godinho, L. +3 · 1 citation
Mathematics · #53D05 #53D20 #57R19 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.AT #math.SG #msc:53D05 #msc:53D20 #msc:57R19

paper · pdf · doi:10.48550/arxiv.math/0505420

15 pages, 3 figures

arxiv created 2005/05/19 · openalex publication_date 2005/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the problem of computing the fundamental group of a symplectic S¹-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 S¹-action. Several examples are presented to illustrate our main results.

Cited by

• THE FUNDAMENTAL GROUP OF G-MANIFOLDS

Related

• π₁ of Hamiltonian S¹ manifolds
• The fundamental group of symplectic manifolds with Hamiltonian SU(2) or SO(3) actions
• Special Hamiltonian S¹-actions on symplectic 4-manifolds
• The fundamental groups of presymplectic Hamiltonian G-manifolds
• Hamiltonian S¹-manifolds which are like a coadjoint orbit of G₂