  We establish an equivariant generalization of the Novikov inequalities which
allow to estimate the topology of the set of critical points of a closed basic
invariant form by means of twisted equivariant cohomology of the manifold. We
apply these inequalities to study cohomology of the fixed points set of a
symplectic torus action. We show that in this case our inequalities are
perfect, i.e. they are in fact equalities.
