Compact Homogeneous Spaces with Positive Euler Characteristic and Their ‘Strange Formulae’

burns, john m; makrooni, mohammad a;

In this note, we prove a generalization of the ‘strange formula’ of Freudenthal and de-Vries for compact homogeneous spaces with positive Euler characteristic. As a corollary, we obtain a new proof of the original formula. We also apply our results to computing a topological invariant used to study hyper-Kähler structures.