# Chern-Weil theorem

From Diffgeom

## Statement

Let denote the Chern form, viz is the Chern form for vector bundle and connection on . Then:

- are closed for all and all
- For all positive integers , there exists a form such that for all on , we have:

Thus, defines an element in independent of . This elements is termed the Chern class (the word *class* because it is a cohomology class).