Steve Halperin – författare
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2 produkter
2 produkter
590 kr
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This book introduces a novel framework to study the rational homotopy of a space through the construction of enriched differential graded Lie algebras (dgls), extending Quillen rational homotopy to non-simply connected spaces in a way that is compatible with the Sullivan minimal models approach. Part I contains the basic theory of enriched Lie algebras and associated quadratic Sullivan algebras. Minimal Sullivan algebras and Sullivan rationalizations are then described in Part II. Part III explores the relations between enriched dgl models, Sullivan models, and topological spaces. The connection between enriched dgls and commutative differential graded algebras (cdgas) is realized using a generalization of the cochain algebra functor. This part contains all the theory necessary for computation of explicit examples and for developing interesting applications. Finally, Part IV concerns inert cell attachments and their applications.
2 140 kr
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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.