Rational homotopy theory II

This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions. This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.

Sequel to Rational homotopy theory (2001), but self contained--Introduction, following table of contents.

1. Basic definitions and constructions. 1.1. Graded algebra. 1.2. Differential graded algebra. 1.3. Simplicial sets. 1.4. Polynomial differential forms. 1.5. Sullivan algebras. 1.6. The simplicial and spatial realizations of a [symbol]-algebra. 1.7. Homotopy and based homotopy. 1.8. The homotopy groups of a minimal Sullivan algebra -- 2. Homotopy Lie algebras and Sullivan Lie algebras. 2.1. The homotopy Lie algebra of a minimal Sullivan algebra. 2.2. The fundamental Lie algebra of a Sullivan 1-algebra. 2.3. Sullivan Lie algebras. 2.4. Primitive Lie algebras and exponential groups. 2.5. The lower central series of a group. 2.6. The linear isomorphism [symbols]. 2.7. The fundamental group of a 1-finite minimal Sullivan algebra. 2.8. The homology Hopf algebra of a 1-finite minimal Sullivan algebra. 2.9. The action of G[symbol] on [symbols]. 2.10. Formal Sullivan 1-algebras.

3. Fibrations and [symbol]-extensions. 3.1. Fibrations, Serre fibrations and homotopy fibrations. 3.2. The classifying space fibration and Postnikov decompositions of a connected CW complex. 3.3. [symbol]-extensions. 3.4. Existence of minimal Sullivan models. 3.5. Uniqueness of minimal Sullivan models. 3.6. The a…