论文标题
头骨型汉密尔顿G-manifolds的基本群体
The fundamental groups of presymplectic Hamiltonian G-manifolds
论文作者
论文摘要
我们认为配备有汉密尔顿g术的前膜歧管，G是一个连接的紧凑型谎言组。预胶片歧管是由前膜形式的核的积分子延伸的。对于预成立的哈密顿G-Manifold，Lin和Sjamaar提出了一种条件，他们表明，MONT MAP图像具有相同的“凸和多面体”属性，与象征性汉密尔顿G-Manifold的矩图图像相同，结果是由Atiyah，Guillemin，Guillemin，Stern-Sternberg和Kirwan的独立证明的。在本文中，在Lin和Sjamaar的条件下提出了有关汉密尔顿二肠g-manifolds的提议，我们研究了这种歧管的基本群体，与早期的结果相比，对象征性汉密尔顿G-manifolds的基本群体进行了比较。我们观察到，符合性案例的结果是预成束案例结果的特殊情况。
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.
