论文标题
Gelfand二元性，用于流形，向量和其他捆绑包
Gelfand duality for manifolds, and vector and other bundles
论文作者
论文摘要
一般而言，Gelfand二元性是指几何，拓扑或分析类别与代数类别之间的对应关系。例如，在平滑的微分几何形状中，Gelfand二元性是指平滑函数代数的拓扑双重偶数中平滑歧管的拓扑嵌入。这是在两个方向上概括的。首先，使用统一的共同体论证，将歧管的拓扑嵌入概括为真实分析和斯坦的歧管的情况。其次，这种双重性扩展到矢量束，仿射束和喷气束，通过使用合适的函数类别，即嵌入嵌入为其值的拓扑二元组。
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a smooth manifold in the topological dual of its algebra of smooth functions. This is generalised here in two directions. First, the topological embeddings for manifolds are generalised to the cases of real analytic and Stein manifolds, using a unified cohomological argument. Second, this type of duality is extended to vector bundles, affine bundles, and jet bundles by using suitable classes of functions, the topological duals in which the embeddings take their values.
