Equivariant bundle

In differential geometry, given a compact Lie group G, an equivariant bundle is a fiber bundle such that the total space and the base spaces are both G-spaces and the projection map ${\displaystyle \pi }$ between them is equivariant: ${\displaystyle \pi \circ g=g\circ \pi }$ with some extra requirement depending on a typical fiber.

For example, an equivariant vector bundle is an equivariant bundle.

References[]

• Berline, Nicole; Getzler, E.; Vergne, Michèle (2004), Heat Kernels and Dirac Operators, Berlin, New York: Springer-Verlag

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