Equivariant bundle

In geometry and topology, given a group G (which may be a topological or Lie group), an equivariant bundle is a fiber bundle $\pi \colon E\to B$ such that the total space $E$ and the base space $B$ are both G-spaces (continuous or smooth, depending on the setting) 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 such that the action of G restricts to a linear isomorphism between fibres.

References

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