Group actions on spin manifolds

Chichilnisky, G.

doi:10.1090/S0002-9947-1972-0309033-4

Group actions on spin manifolds
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by G. Chichilnisky PDF

Trans. Amer. Math. Soc. 172 (1972), 307-315 Request permission

Abstract:

A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincaré group $\mathcal {P}$ of a Lorentz manifold $M$. It is shown that the topological restrictions needed to lift an action in $\mathcal {P}$ are more stringent than for actions in the proper Poincaré group $\mathcal {P}_ \uparrow ^ +$. Similar results hold for the Euclidean group of a Riemannian manifold.

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