[Math] the best way to study Rational Homotopy Theory

at.algebraic-topologyrational-homotopy-theory

I studied basic algebraic topology elements:

fundamental group, higher homotopy groups, fibre bundles, homology groups, cohomology groups, obstruction theory, etc.

I want to study Rational Homotopy Theory.

Specifically, I want to study Sullivan's model.

What is the short way and what is the complete way to study Sullivan's model?

Best Answer

Griffiths and Morgan wrote a fine book on the subject. Apart from the obvious attractiveness of learning a theory from its creator, it is written in an amazingly user-friendly style. For example, Chapter XIII is devoted to examples and computations: it starts with the computation of a minimal model for the forms on a sphere and ends with Massey triple products on compact Kähler manifolds, a section inspired by the 1974 Inventiones article of Deligne,Griffiths, Morgan, Sullivan. The first hundred pages (Chapters I to VII) are an introduction to the necessary algebraic topology and you can probably essentially skip it, judging from your description of what you already know.

Reference Griffiths, P.; Morgan, J. (1981), Rational homotopy theory and differential forms, Progress in Mathematics, 16, Birkhäuser