A Universal Property of the Groups Spinc and Mpc
Abstract
It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spinc structures are often introduced. In this paper we prove that spinc structures have a universal property among all other structures that enable the construction of spinor bundles. We proceed to prove a similar result for metaplecticc structures on symplectic manifolds.
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