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We demonstrate that it is conceptually and computationally favorable toregard spin-weighted spherical harmonics as vector valued functions on thetotal space $SO(3)$ of the Hopf bundle, satisfying a covariance condition withrespect to the gauge group $U(1)$ of this bundle. A key role is played by theinvariant connection form of the principle Hopf bundle, known to physicistsfrom the geometry behind magnetic monopoles.

Geometry of the Hopf Bundle and spin-weighted Harmonics