Cliiord Structures and Spinor Bundles
نویسنده
چکیده
It is shown that every bundle ! M of complex, irreducible and faithful modules over the Cliiord bundle of an even-dimensional Riemannian space (M; g) with local model (V; h) is associated with a cpin (\Cliiord") structure on M, this being an extension of the SO(h)-bundle of orthonormal frames on M to the Cliiord group Cpin(h) = (C Spin(h))=Z 2. An explicit construction is given of the total space of the Cpin(h)-bundle deening such a structure. A canonical line bundle on a cpin man-ifold, associated with the spinor norm homomorphism, is identiied with a subbundle of Hom(;). The cpin structure restricts to a spin structure ii this line bundle is trivial.
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