平坦丛的上同调与一个Chern-Simons泛函
Cohomology of flat bundles and a Chern-Simons functional
摘要：
证明了具有紧连通结构群的平坦主丛及其李群的伴随丛与平凡丛具有相同的上同调，这是通过证明它们满足Leray-Hirsch定理的条件来实现的.这一信息已被用来构造一个平坦丛的伴随丛的上同调类，其对每个纤维的限制是Maurer-Cartan 3-形式的类。然后，我们使用这个结果来定义一个不变量的规范变换的平坦丛描述的效果的规范变换上的Chern-Simons功能。
英文摘要：
We show that a flat principal bundle with compact connected structure group and its adjoint bundles of Lie groups have the same cohomology as the trivial bundle, which is done by proving they satisfy the condition for the Leray-Hirsch theorem. This information has been used to construct a cohomology class of the adjoint bundle of a flat bundle whose restriction to each fiber is the class of the Maurer-Cartan 3-form. Then we use this result to define an invariant of a gauge transformation of a flat bundle which describes the effect of the gauge transformation on a Chern-Simons functional.
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