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.

References in corpus (5)

• An exotic sphere with positive sectional curvature
• A positively curved manifold homeomorphic to T${}_1$S${}^4$
• Geometric formality of homogeneous spaces and of biquotients
• Non-formal compact manifolds with small Betti numbers
• Computational complexity of topological invariants