Ingeometry and topology, given a group G (which may be a topological or Lie group), an equivariant bundle is a fiber bundle such that the total space
and the base space
are both G-spaces (continuous or smooth, depending on the setting) and the projection map
between them is equivariant:
with some extra requirement depending on a typical fiber.
For example, an equivariant vector bundle is an equivariant bundle such that the action of G restricts to a linear isomorphism between fibres.
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