Abstract:
We start with a manifold B. In this project, we are interested in figuring out the multiplicative group generated by the total Chern Classes of all complex vector bundles over B. We call it the "Chern Group" of B and denote it by C(B). We describe these groups for familiar spaces, for example, spheres & tori. We will also inspect the analogous subgroup W(B), generated by the total Stiefel-Whitney Classes.
