A global perspective to connections on principal 2-bundles
A global perspective to connections on principal 2-bundles
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DOI：
10.1515/forum-2017-0097
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发表时间：
2016-08
影响因子：
0.8
通讯作者：
K. Waldorf
中科院分区：
文献类型：
--
作者：
K. Waldorf
对于严格的Lie 2-群，我们提出了Lie 2-代数值微分形式的概念，给出了一个微分分次交换Lie代数，它具有Lie 2-群的伴随作用和Lie 2-群之间沿着Morita等价的拉回运算.利用这个概念，我们定义主2-丛上的联络为2-丛的全空间李群胚上的李2-代数值1-形式，满足与普通主丛上的联络完全类似的条件。我们仔细对待各种概念的曲率，并证明了分类结果的非交换微分上同调的Breen-Messing。这为更高规范理论提供了一个一致的、全局的视角。
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen–Messing. This provides a consistent, global perspective to higher gauge theory.