Integration of generalized complex structures
Integration of generalized complex structures
复制标题
广义复杂结构的集成
DOI：
10.1063/5.0091245
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发表时间：
2016
影响因子：
1.3
通讯作者：
M. Gualtieri
中科院分区：
文献类型：
--
作者：
M. Bailey;M. Gualtieri
求解广义复流形的积分问题，得到具有位移辛结构的全纯堆栈作为自然积分对象；换句话说，具有相容复结构的实辛群只在Morita等价下才有定义。我们解释了这些对象如何微分得到广义复流形，并证明了广义复流形在这种意义上是可积的，当且仅当其底层的实泊松结构是可积的。我们将描述这些集成的几个具体示例。对我们的解决至关重要的是新的技术工具，它们是独立感兴趣的，即Courant代数上李群类群作用的约简过程，以及局部李群类群上乘法形式的某些局部到全局的推广结果。
We solve the integration problem for generalized complex manifolds, obtaining as the natural integrating object a holomorphic stack with a shifted symplectic structure; in other words, a real symplectic groupoid with a compatible complex structure is defined only up to Morita equivalence. We explain how such objects differentiate to give generalized complex manifolds, and we show that a generalized complex manifold is integrable in this sense if and only if its underlying real Poisson structure is integrable. We describe several concrete examples of these integrations. Crucial to our solution are new technical tools, which are of independent interest, namely, a reduction procedure for Lie groupoid actions on Courant algebroids, as well as certain local-to-global extension results for multiplicative forms on local Lie groupoids.