Sheaf of connection algebras
This article defines a sheaf that can be associated to a differential manifold. The global analog of this sheaf, which is also the same as the object of the sheaf associated to the whole manifold, is: connection algebra
Let be a differential manifold. The sheaf of connection algebras of is defined as follows:
- For every open subset of , the object associated to is the connection algebra associated to , viewed as a manifold.
- The restriction map is defined using the natural restriction map for the sheaf of first-order differential operators, and the sheaf of infinitely differentiable functions
Sometimes the sheaf of connection algebras is termed the connection algebra, though the latter term is sometimes used for the global object.