Mathematische Zeitschrift

, Volume 274, Issue 3–4, pp 1299–1325 | Cite as

Non-formal homogeneous spaces



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.


Homogeneous space Non-formal manifold 

Mathematics Subject Classification (2000)

Primary 57N65 Secondary 57T15 57T20 



The author is very grateful to Anand Dessai for various fruitful discussions and to Jim Stasheff for commenting on a previous version of this article. The author would also like to thank the referee for several helpful suggestions.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics, David Rittenhouse LaboratoryUniversity of PennsylvaniaPhiladelphiaUSA

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