Iterated Peiffer pairings in the Moore complex of a simplicial group

TL;DR

This paper introduces a pairing structure in the Moore complex of a simplicial group to analyze generators of certain subgroups, advancing algebraic models for homotopy types.

Contribution

It presents a novel pairing structure within the Moore complex of simplicial groups, providing new tools for studying generators related to degenerate elements.

Findings

Identified generators for NG_n ∩ D_n using the pairing structure

Applied the pairing to develop algebraic models for homotopy types

Enhanced understanding of the Moore complex in simplicial groups

Abstract

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NG_n\cap D_n where D_n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.