Spinors and diffeomorphisms (Q1083707)

The authors investigate the action of diffeomorphisms on spinors on an oriented manifold M. They first describe the action of the diffeomorphism group D(M) on the set of inequivalent spinor structures and prove that it is affine. It is argued that the existence of spinors in the gauge group of gravity is a certain double cover of D(M) depending on the spin structure. The explicit action of D(M) on the set of inequivalent spin structures is discussed in detail when M is a closed Riemann surface.