Equivariant bundle explained

\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