Supergeometry in Equivariant Cohomology

@inproceedings{ANersessian1998SupergeometryIE,
  title={Supergeometry in Equivariant Cohomology},
  author={A.Nersessian},
  year={1998}
}
We analyze $S^1$ equivariant cohomology from the supergeometrical point of view. For this purpose we equip the external algebra of given manifold with equivariant even super(pre)symplectic structure, and show, that its Poincare-Cartan invariant defines equivariant Euler classes of surfaces. This allows to derive localization formulae by use of superanalog of Stockes theorem.