Algebraic models for equivariant rational homotopy theory for discrete groups

TL;DR

This paper develops algebraic models for equivariant rational homotopy theory with discrete groups, extending existing models to the genuine equivariant setting and comparing different algebraic frameworks.

Contribution

It introduces a generalized algebraic framework for equivariant rational homotopy theory applicable to discrete groups, including cdga and Lie algebra models.

Findings

Provides a unified algebraic framework for equivariant rational homotopy theory.

Extends models to the genuine equivariant case for discrete groups.

Compares cdga models with other existing models in the literature.

Abstract

We provide a framework which generalizes algebraic models of a homotopy theory of spaces to the genuine equivariant case for a discrete group. We explain how this applies to commutative differential graded algebra (cdga) models and complete differential graded Lie algebra models for rational spaces. We compare the cdga model to other model categories in the literature.