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Lie models for spaces a new approach to rational homotopy

"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 approac...

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Bibliographic Details
Main Authors: Félix, Y. (Yves) (Author), Halperin, Stephen (Author)
Format: eBook
Language:English
Published: Cham, Switzerland Birkhäuser [2026]
Series:Frontiers in mathematics.
Subjects:
Homotopía
Álgebras de Lie
Topología algebraica
Homotopy theory
Lie algebras
Algebraic topology
Lie algebras.
Homotopy theory.
Electronic books.
Table of Contents:
  • Enriched and pre-enriched Lie algebras
  • Enriched vector spaces
  • Lower central series
  • The quadratic Sullivan model of an enriched Lie algebra
  • Representations of enriched Lie algebras
  • Profree Lie algebras
  • Sullivan rational homotopy theory
  • The homotopy Lie algebra Lv of a minimal Sullivan algebra
  • The Sullivan rationalization, Xq, of a space X
  • Sullivan rational spaces
  • Enriched dgl's and semi-quadratic Sullivan algebras
  • Profree dgl's and profree dgl models
  • The model category of enriched dgl's
  • The profree dgl model of a cdga and of a topological space
  • Topological cell attachments
  • Inert attachments
  • Applications in topology