论文标题
在差异矢量伪捆绑和无限尺寸矢量束的几何形状上：自动形态，连接和协变量衍生物
On the geometry of diffeological vector pseudo-bundles and infinite dimensional vector bundles: automorphisms, connections and covariant derivatives
论文作者
论文摘要
我们在这里考虑了差异矢量伪捆绑的类别，并研究了经典差异几何工具在有限尺寸尺寸矢量束上的可能扩展，即，框架束，连接1形的空间和协证衍生物的空间。在这个广义框架中强调了未成年区分，其中1形和协变量衍生物之间的非同态性别。应用不仅包括具有奇异性的有限维度示例，还包括无限的尺寸矢量束。
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the space of connection 1-forms and the space of covariant derivatives. Substential distinctions are highlighted in this generalized framework, among which the non-isomorphism between connection 1-forms and covariant derivatives. Applications not only include finite dimensional examples with singularities, but also infinite dimensional vector bundles.
