A note on the splitting principle
J.P. May
may@math.uchicago.edu
55R40, 55N99

We offer a new* perspective on the splitting principle.
We give an easy proof that applies to all classical 
types of vector bundles and in fact to $G$-bundles for 
any compact connected Lie group $G$. The perspective
gives precise calculational information and directly 
ties the splitting principle to the specification of 
characteristic classes in terms of classifying spaces.

* Note to the list: if this is not new, please let me 
know --- it shouldn't be, but it was to those experts 
I tried it out on.