Group-cohomology refinement to classify $G$-symplectic manifolds

TL;DR

This paper introduces a group-cohomology refinement called pseudo-cohomology to classify G-symplectic manifolds, providing new insights through symplectic cohomology that extend previous Cartan-Eilenberg cohomology methods.

Contribution

It develops a refined cohomology framework that enhances the classification of G-symplectic manifolds beyond traditional methods.

Findings

Pseudo-cohomology effectively classifies G-symplectic manifolds.

Symplectic cohomology offers new analytical tools.

The approach extends Cartan-Eilenberg cohomology insights.

Abstract

``Pseudo-cohomology'', as a refinement of Lie group cohomology, is soundly studied aiming at classifying of the symplectic manifolds associated with Lie groups. In this study, the framework of symplectic cohomology provides fundamental new insight, which enriches the analysis previously developed in the setting of Cartan-Eilenberg $H^2(G,U(1))$ cohomology.