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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.
A cohomological obstruction to weak approximation for homogeneous spaces
Brauer-Manin obstruction weak approximation homogeneous spaces
2011/1/19
Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H G is a k-subgroup (not necessarily con-nected). Let S be a finite set of places of k...