Unbased rational homotopy theory: a Lie algebra approach

TL;DR

This paper develops an algebraic framework for unbased rational homotopy theory using curved Lie algebras, establishing a Quillen equivalence with commutative differential graded algebras, thus extending existing algebraic models.

Contribution

It introduces a model structure for pseudo-compact curved Lie algebras and proves its Quillen equivalence to unital commutative differential graded algebras, expanding the algebraic tools for homotopy theory.

Findings

Constructed a model structure for curved Lie algebras

Established Quillen equivalence with commutative differential graded algebras

Extended known algebraic models for rational homotopy theory

Abstract

In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with curved morphisms will be introduced; one which is Quillen equivalent to a certain model structure of unital commutative differential graded algebras, thus extending the known Quillen equivalence of augmented algebras and differential graded Lie algebras.