On non-formality of homogeneous spaces

TL;DR

This paper investigates the property of formality in rational homotopy theory, demonstrating that certain homogeneous spaces do not possess this property, which has implications for their topological structure.

Contribution

The paper proves the non-formality of specific families of homogeneous spaces, advancing understanding of their rational homotopy properties.

Findings

Certain homogeneous spaces are proven to be non-formal.

The results contribute to the classification of spaces based on formality.

Implications for the study of topological and geometric properties of these spaces.

Abstract

One of the interesting and important rational homotopy properties of a topological space $X$ is that of {\em formality}. In this paper we prove the non-formality property of some family homogeneous spaces.