On cohomological decomposition of generalized-complex structures

TL;DR

This paper investigates how generalized-complex structures influence cohomological decomposition, unifying concepts from complex and symplectic geometry, with explicit examples on the Iwasawa manifold.

Contribution

It introduces a unified approach to cohomological decomposition via generalized-complex structures, encompassing pure-and-fullness and Hard Lefschetz conditions.

Findings

Examples on the Iwasawa manifold illustrate the theory.

Connections between complex and symplectic cases are established.

New insights into cohomological properties of generalized structures.

Abstract

We study properties concerning decomposition in cohomology by means of generalized-complex structures. This notion includes the $\mathcal{C}^\infty$-pure-and-fullness introduced by Li and Zhang in the complex case and the Hard Lefschetz Condition in the symplectic case. Explicit examples on the moduli space of the Iwasawa manifold are investigated.