Non-formal Homogeneous Spaces

TL;DR

This paper explores the construction and characterization of non-formal homogeneous spaces, demonstrating their existence in every dimension from 72 onwards, thus expanding the known landscape of such spaces.

Contribution

It introduces new principles and criteria for constructing non-formal homogeneous spaces, significantly broadening the known examples in the field.

Findings

Non-formal homogeneous spaces exist in every dimension from 72 onwards

New construction principles for non-formal spaces are established

A large class of examples of non-formal homogeneous spaces is provided

Abstract

Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known. In this article we provide several construction principles and characterisations for non-formal homogeneous spaces, which will yield a lot of examples. This will enable us to prove that, from dimension 72 on, such a space can be found in each dimension.