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Equivariant bundle

From Wikipedia, the free encyclopedia

In geometry 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.

References

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