2022/08/25 by Yves Félix, Félix, Yves, Halperin, Steve
Mathematics · #55P62 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2208.12171
openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a new category, Edgl, of enriched differential graded Lie algebras (edgl), directly related to the topology of all connected CW complexes and simplicial sets. It is equipped with a homotopy theory analogous to that developed by Sullivan for commutative differential graded algebras. Each connected space has a unique minimal edgl model, and an algebraic process connects this to the minimal Sullivan model. Minimal edgl models naturally represent cofibrations and, in particular cell attachments, and the interplay between edgl and Sullivan models permits the extension to all path connected spaces of results previously established only for simply connected spaces. This, in particular, provides applications and interesting examples of the classical Sullivan rationalization X→ X\mathbb Q of a path connected space.