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 \pi between them is equivariant: \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.

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