The fundamental groups of presymplectic Hamiltonian G-manifolds

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.