In
geometry and
topology, given a
group ''G'', an equivariant bundle is a
fiber bundle
In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space E and a p ...
such that the total space and the base spaces are both
''G''-spaces and the projection map
between them is equivariant:
with some extra requirement depending on a typical fiber.
For example, an
equivariant vector bundle In mathematics, given an action \sigma: G \times_S X \to X of a group scheme ''G'' on a scheme ''X'' over a base scheme ''S'', an equivariant sheaf ''F'' on ''X'' is a sheaf of \mathcal_X-modules together with the isomorphism of \mathcal_-modules
...
is an equivariant bundle.
References
*Berline, Nicole; Getzler, E.; Vergne, Michèle (2004), Heat Kernels and Dirac Operators, Berlin, New York: Springer-Verlag
Fiber bundles
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