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This paper reviews some recent work on (s)pin structures and the Diracoperator on hypersurfaces (in particular, on spheres), on real projectivespaces and quadrics. Two approaches to spinor fields on manifolds are compared.The action of space and time reflections on spinors is discussed, also fortwo-component (chiral) spinors.Comment: 10 pages, 1 figure, AMS-LaTe

Reflections and spinors on manifolds