Basic Forms and Orbit Spaces:a Diffeological Approach
Basic Forms and Orbit Spaces:a Diffeological Approach
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DOI：
10.3842/sigma.2016.026
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发表时间：
2014-08
影响因子：
0.9
通讯作者：
Yael Karshon;J. Watts
中科院分区：
文献类型：
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作者：
Yael Karshon;J. Watts
如果一个李群自由且适当地作用在一个流形上，那么通过商映射拉回，给出了商流形上的微分形式与上面的基本微分形式之间的同构。我们表明，这一结果仍然是真实的行动，不一定是自由的，也不适当的，只要单位分量的行为正常，在商空间上，我们采取微分形式在代数意义上。
If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.