total chern class = c(F)= . The determinant is a sum of forms of different orders: where is a 2j-form.

G compact means F is anti-hermitian real differential form.

is hermitian so can be diagonalized by a unitary transformation.

this means where the 's are 2-forms.

This means

For the second churn class, you get:

properties:

- 2 vector bundles, and over same base M, do whitney sum, , then
- splitting principle

source

psfile jl@crush.caltech.edu index

character_class_example

splitting_principle