Characteristic classes of vector bundles with extra structure

TL;DRAbstract

This work is about properties of characteristic cohomology classes which occur when a special structure on vector bundles is given. I have focused on two different types of these structures, treated in two independent parts. The first part uses orientation and spin structure, and follows the literature in this area, mainly [Baum] and in the Riemannian section [Lawson & Michelsohn], with some remarks. Two open questions are left in it, on pages 23 and 27. The second part uses complex structure and follows an idea on which I haven"t found literature so far. The section 2.5 about almost complex spin manifolds on page 26 gives the link between the two parts. For the construction of all the characteristic classes I use, I refer to [Milnor & Stasheff].

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