Divided power structures and chain complexes

TL;DR

This paper explores the relationship between divided power structures on homotopy groups of simplicial commutative rings and analogous structures on chain complexes, using a non-standard symmetric monoidal framework.

Contribution

It introduces a novel interpretation linking divided power structures in homotopy groups to those in chain complexes via a new symmetric monoidal structure.

Findings

Established a correspondence between divided power structures on homotopy groups and chain complexes.

Developed a non-standard symmetric monoidal structure for chain complexes.

Provided a new perspective on algebraic structures in homotopy theory.

Abstract

We interpret divided power structures on the homotopy groups of simplicial commutative rings as having a counterpart in divided power structures on chain complexes coming from a non-standard symmetric monoidal structure.