Equivariant Ω

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.

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:

(7)

satisfies