The fundamental groups of presymplectic Hamiltonian G-manifolds
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866929534298750976 |
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| author | Li, Hui |
| author_facet | Li, Hui |
| contents | We consider presymplectic manifolds equipped with Hamiltonian G-actions, G being a connected compact Lie group. A presymplectic manifold is foliated by the integral submanifolds of the kernel of the presymplectic form. For a presymplectic Hamiltonian G-manifold, Lin and Sjamaar propose a condition under which they show that the moment map image has the same "convex and polyhedral" property as the moment map image of a symplectic Hamiltonian G-manifold, a result proved independently by Atiyah, Guillemin-Sternberg, and Kirwan. In this paper, under the condition Lin and Sjamaar proposed on presymplectic Hamiltonian G-manifolds, we study the fundamental groups of such manifolds, comparing with earlier results on the fundamental groups of symplectic Hamiltonian G-manifolds. We observe that the results on the symplectic case are special cases of the results on the presymplectic case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_08062 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The fundamental groups of presymplectic Hamiltonian G-manifolds Li, Hui Symplectic Geometry Algebraic Topology We consider presymplectic manifolds equipped with Hamiltonian G-actions, G being a connected compact Lie group. A presymplectic manifold is foliated by the integral submanifolds of the kernel of the presymplectic form. For a presymplectic Hamiltonian G-manifold, Lin and Sjamaar propose a condition under which they show that the moment map image has the same "convex and polyhedral" property as the moment map image of a symplectic Hamiltonian G-manifold, a result proved independently by Atiyah, Guillemin-Sternberg, and Kirwan. In this paper, under the condition Lin and Sjamaar proposed on presymplectic Hamiltonian G-manifolds, we study the fundamental groups of such manifolds, comparing with earlier results on the fundamental groups of symplectic Hamiltonian G-manifolds. We observe that the results on the symplectic case are special cases of the results on the presymplectic case. |
| title | The fundamental groups of presymplectic Hamiltonian G-manifolds |
| topic | Symplectic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2004.08062 |