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.Contents:

Basic Definitions and Constructions
Homotopy Lie Algebras and Sullivan Lie Algebras
Fibrations and Λ-Extensions
Holonomy
The Model of the Fibre is the Fibre of the Model
Loop Spaces and Loop Space Actions
Sullivan Spaces
Examples
Lusternik-Schnirelmann Category
Depth of a Sullivan Algebra and of a Sullivan Lie Algebra
Depth of a Connected Graded Lie Algebra of Finite Type
Trichotomy
Exponential Growth
Structure of a Graded Lie Algebra of Finite Depth
Weight Decompositions of a Sullivan Lie Algebra
ProblemsKey Features:

Contains the basis for using rational homotopy theory for non-simply connected spaces
Contains new important information on the rational homotopy Lie algebra of spaces
Is at the frontier of the research in rational homotopy