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.
Read more about this topic: Quaternionic Projective Space
Famous quotes containing the word space:
“At first thy little being came:
If nothing once, you nothing lose,
For when you die you are the same;
The space between, is but an hour,
The frail duration of a flower.”
—Philip Freneau (1752–1832)