Non-formal homogeneous spaces

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.