Marc A. Rieffel
Published 2007-03-16, updated 2008-11-14Version 5
In order to facilitate the comparison of Riemannian homogeneous spaces of compact Lie groups with noncommutative geometries ("quantizations") that approximate them, we develop here the basic facts concerning equivariant vector bundles and Dirac operators over them in a way that uses only global constructions and arguments. Our approach is quite algebraic, using primarily the modules of cross-sections of vector bundles. We carry the development through the construction of Hodge--Dirac operators. The inducing construction is ubiquitous.
Comments: 20 pages. An error in the proof of theorem 8.4 of the published version is corrected, resulting also in a stronger theorem. A few minor improvements elsewhere
Journal: Contemporary Math. 449 (2008), 399-415
Covering maps and ideal embeddings of compact homogeneous spaces
Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces
Classification of compact homogeneous spaces with invariant $G_2$-structures
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