Lie Models for Spaces

A New Approach to Rational Homotopy

von Yves Félix, Steve Halperin

206 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Frontiers in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Topologie Algebraische Topologie
• ISBN: 9783032153562
• Sprache: Englisch
• Erscheinungsdatum: 25.02.2026
• Größe: 24 x 16.8 cm
• Verlag: Springer International Publishing