  Which spaces look like an n-sphere through the eyes of the n-th Postnikov
section functor and the n-connected cover functor? The answer is what we call
the Postnikov genus of the n-sphere. We define in fact the notion of
localization genus for any homotopical localization functor in the sense of
Bousfield and Dror Farjoun. This includes exotic genus notions related for
example to Neisendorfer localization, or the classical Mislin genus, which
corresponds to rationalization.
