Adrian Dobson (University of Manchester)
adobson@maths.manchester.ac.uk
Given a complex vector bundle whose base has cells in only even dimensions, we express the KO-theory of the Thom complex as a module over the KO-theory of the base. In general, the absence of a Thom class means this is not a module on a single generator. Our calculations make use of an exact sequence due to Bott, relating real and complex K-theory via natural homomorphisms.