A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces

Details A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces

2007-03-16

arxiv.org/abs/math/0703496v5

Contemporary Math. 449 (2008), 399-415

Mathematics

Differential Geometry

20 pages. An error in the proof of theorem 8.4 of the published version is corrected, resulting also in a stronger theorem. A

Scientific paper

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.

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