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1 Cartan model of equivariant cohomology
2 Equivariant analogue of

Equivariant analogue of
We can now construct the equivariant analogue of using the Cartan model of equivariant cohomology.

It will be equivariant with respect to some subalgebra of symmetries which we will describe shortly.

1 Cartan model of equivariant cohomology

complex as a linear space: 

differential: 

We will restrict the Lie algebra of symmetries so that for any we can solve the following equation for :

or equivalently:

notice that this implies: 

2 Equivariant analogue of

(7)

satisfies