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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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Loopspace of an Eilenberg Maclane space K(G,n)

I've seen the fact that the loopspace $\Omega K(G,n)$ is homotopy equivalent to $K(G,n-1)$ mentioned in some places, but I have no idea why. Can anyone offer a good explanation? Also, what happens w …
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