6 papers
A new approach to rational stable parametrized homotopy theory
Yves Félix, Aniceto Murillo, Alejandro Saiz
This work develops a comprehensive algebraic model for rational stable parametrized homotopy theory over arbitrary base spaces. Building on the simplicial analogue of the foundatio…
A Lie characterization of the Bousfield-Kan -completion and -good spaces
Yves Félix, Mario Fuentes, Aniceto Murillo
We prove that the unit of the Quillen pair given by the model and realization functor i…
Rational homotopy type of relative universal fibrations
Yves Félix, Mario Fuentes, Aniceto Murillo
For any group of self homotopy equivalences of the finite nilpotent complex , acting nilpotently on its homology, and for any nilpotent subcomplex , we prove that the uni…
Enriched Differential Lie Algebras in Topology
Yves Félix, Steve Halperin
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.…
All known realizations of complete Lie algebras coincide
Yves Félix, Mario Fuentes, Aniceto Murillo
We prove that for any reduced differential graded Lie algebra L, the classical Quillen geometrical realization is homotopy equivalent to the realization $\lang…
Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types
Yves Félix, Mario Fuentes, Aniceto Murillo
We construct Lie algebras of derivations (and identify their geometrical realization) whose Maurer-Cartan sets provide moduli spaces describing the classes of homotopy types of rat…