Binomial rings and homotopy theory

TL;DR

This paper develops an algebraic model for integral homotopy types using cosimplicial binomial rings, and constructs an integral Grothendieck-Teichmüller group, bridging homotopy theory and algebra.

Contribution

It introduces a fully faithful functor from nilpotent spaces to cosimplicial binomial rings, providing a new algebraic framework for integral homotopy types.

Findings

Established a correspondence between nilpotent spaces and binomial rings

Constructed an integral Grothendieck-Teichmüller group

Provided new tools for algebraic modeling of homotopy types

Abstract

We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application, we construct an integral version of the Grothendieck-Teichm\"uller group.