Novikov inequalities with symmetry
  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 1-form by means of twisted equivariant cohomology of the manifold. We test and apply our inequalities in the case of a finite group.   As an application we obtain Novikov type inequalities for a manifold with boundary. 
Maxim Braverman and Michael Farber