Equivariant Novikov inequalities

TL;DR

This paper generalizes Novikov inequalities to equivariant settings, enabling topological estimates of critical points of invariant forms and applying these results to symplectic torus actions, where the inequalities become equalities.

Contribution

It introduces an equivariant version of Novikov inequalities and demonstrates their exactness in symplectic torus actions.

Findings

Established equivariant Novikov inequalities for invariant forms.

Applied inequalities to symplectic torus actions, showing they are perfect.

Provided new tools for analyzing critical points via twisted equivariant cohomology.

Abstract

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.