Classifying Spinor Structures (abstract)

From ScottWiki

I begin by introducing and motivating the definition of a spinor structure in terms of familiar geometrical ideas.

The central result of this thesis is a complete and constructive classification of spinor structures, generalising some earlier results. I will explain how principal fibre bundles and covering spaces provide the key ingredients to the proof. A different type of classification can also be attempted, in terms of the underlying principal fibre bundle, and this allows us to compare `spinor connections'.

I'll also mention briefly how spinor structures for Lorentzian manifolds provide the natural setting for the `spinor calculus', and so for the Dirac equation for the electron.