Rational Homotopy Theory II

Description

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 Content: Sullivan Model and Rationalization of a Non-Simply Connected Space Homotopy Lie Algebra of a Space and Fundamental Group of the Rationalization, Model of a Fibration Holonomy Operation in a Fibration Malcev Completion of a Group and Examples Lusternik-Schnirelmann Category Depth of a Sullivan Lie Algebra Growth of Rational Homotopy Groups Structure of Rational Homotopy Lie Algebras Weighted Lie Algebras