Talk:Rational homotopy theory

I have changed the definition of Formal spaces in a significant way. I believe that the way the page was before was confusing and wrong.

For a formal space, its cohomology algebra should be a model for it. The question is whether it has to be the minimal model (rather than just a cdga model). I believe that the answer is no -- for example, even spheres are formal, but their minimal model is not their cohomology. In fact, if a space's minimal model is its cohomology, it must be a free alternating algebra on some generators. (Every minimal model is a Sullivan model, and thus is a free alternating algebra. If we assume it is also the cohomology, the differential has to be 0 as well). The only such spaces are products of Eilenberg-Maclane spaces.

I am not an expert on this, though, but please enlighten me if this is a mistake.

199.168.74.114 (talk) 21:35, 22 November 2014 (UTC) Ilya.

Todo

 * Add additional motivation for rational homotopy theory
 * Cleanup notation and improve organization
 * https://www.math.ias.edu/~lurie/ThursdayFall2017/Lecture1-Overview.pdf has an excellent overview of the ideas of the subject, they should be integrated into this page — Preceding unsigned comment added by Wundzer (talk • contribs) 18:03, 10 June 2020 (UTC)