6
$\begingroup$

It is well known that for simply-connected rational spaces, every suspension splits as a wedge of rational spheres and every loop space splits as a product of rational Eilenberg-Mac Lane spaces.

What are the best/original references for this?

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ Sorry, I don't know of a reference, but using algebraic models is very easy. Let's say DGL algebras, so as not to exclude the rational spaces with infinite-dimensional homotopy groups. The suspension of a DGL algebra whose underlying Lie algebra is free can be easily seen to have trivial differentials, since in the cilinder all diferentials are supported by the boundary, hence the claim follows. $\endgroup$
    – Fernando Muro
    Commented May 4, 2012 at 11:18

0

Reset to default

You must log in to answer this question.