Infinite-dimensional Quaternionic Projective Space
The space is the classifying space BS3. The homotopy groups of are given by . These groups are known to be very complex and in particular they are non-zero for infinitely many values of . However, we do have that if and if . It follows that rationally, i.e. after localisation of a space, is an Eilenberg–Maclane space . That is . (cf. the example K(Z,2)). See rational homotopy theory.
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