Leray-Hirsch theorem for K-theory
From Topospaces
Statement
Let be a fiber bundle with both and compact Hausdorff spaces and with fiber space , such that :
- is free and finitely generated
- There exist classes that restrict to a freely generating set for for each fiber
And suppose one of these conditions holds:
- is a finite cell complex
- is a finite cell complex having only cells of even dimension
Then is free as a module over , with basis .
References
- Vector bundles and K-theory by Allen Hatcher