Abstract
Equivariant cohomology is a structure which is attached to a smooth effective action of a Lie group G on a smooth manifold P. The model of Henri Cartan [16] for it is a variation of de Rham cohomology, in which the algebra Ω*(P) of smooth complex-valued differential forms on P is replaced by the algebra
of G-equivariant polynomial mappings α
from the Lie algebra g of G to Ω*(P). The equivariance of α means that
Here, for g ∈ G, Adg is the adjoint action of conjugation by g on the Lie algebra g, and g *P denotes the pullback of differential forms by means of the action gP : P → P of g on P.
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© 1996 Birkhäuser Boston
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Duistermaat, J.J. (1996). Appendix: Equivariant Forms. In: The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Progress in Nonlinear Differential Equations and their Applications, vol 18. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5344-0_16
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DOI: https://doi.org/10.1007/978-1-4612-5344-0_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-5346-4
Online ISBN: 978-1-4612-5344-0
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