Minimal models of some differential graded modules

TL;DR

This paper introduces a new Koszul operad to unify various operadic approaches in constructing minimal models of chain complexes related to free torus actions, advancing the algebraic framework in this area.

Contribution

It defines a novel Koszul operad that projects onto existing operads used in minimal model constructions for chain complexes of free torus actions.

Findings

Introduces a new Koszul operad with projections onto existing operads.

Provides a unified operadic framework for minimal models.

Enhances algebraic tools for studying chain complexes in topology.

Abstract

Minimal models of chain complexes associated with free torus actions on spaces have been extensively studied in the literature. In this paper, we discuss these constructions using the language of operads. The main goal of this paper is to define a new Koszul operad that has projections onto several of the operads used in these minimal model constructions.