Strong formality of toric and homogeneous compact K\"ahler manifolds

TL;DR

This paper investigates the formality properties of compact Kähler manifolds, demonstrating that certain classes like toric and homogeneous manifolds are both rationally and strongly formal, unlike the general case.

Contribution

It establishes that complete smooth complex toric varieties and homogeneous compact Kähler manifolds are both rationally and strongly formal, extending understanding of their topological properties.

Findings

Toric varieties are strongly formal.

Homogeneous compact Kähler manifolds are strongly formal.

Not all compact Kähler manifolds are strongly formal.

Abstract

All compact K\"ahler, or even $\partial\bar\partial$-manifolds, are rationally formal. Not all of them are strongly formal. Yet some of them are: For complete smooth complex toric varieties and homogeneous compact K\"ahler manifolds we show the stronger property that they are both rationally and strongly formal in a compatible way.