论文标题
QP-Manifolds的正式指数和线性化
Formal exponentials and linearisations of QP-manifolds
论文作者
论文摘要
我们将任何分级歧管的形式指数图定义为正式切线束（我们也将其定义）中的地图定义为分级歧管。我们表明，每个这样的映射都唯一地决定并取决于其相关的Grothendieck连接，该连接被证明是平坦的，并提供了函数环的分辨率。然后，我们展示了涉及切线束上连接数据的最新结构如何在我们的定义中恢复大量的正式指数。 作为一个应用程序，我们使用正式的指数映射在某个点线性化QP-manifold。这为每个点提供了正式的切线空间，具有不变的内部产品的$ L_ \ infty $ - 代数的结构。
We define formal exponential maps for any graded manifold as maps from the formal tangent bundle (that we also define) into the graded manifold. We show that each such map uniquely determines and is determined by its associated Grothendieck connection, which is shown to be flat, and to furnish a resolution of the ring of functions. We then show how a recent construction involving the data of a connection on the tangent bundle recovers a large class of formal exponentials in our definition. As an application, we use a formal exponential map to linearise a QP-manifold at a point. This gives the formal tangent space at each point the structure of an $L_\infty$-algebra with invariant inner product.
