Peiffer Elements in the Moore Complex of a Bisimplicial Group

TL;DR

This paper explores Peiffer pairings within the Moore complex of bisimplicial groups and demonstrates their applications to the theory of crossed modules and squares, advancing understanding of algebraic structures in higher dimensions.

Contribution

It provides a detailed explanation of Peiffer pairings in bisimplicial groups and introduces their applications to crossed modules and crossed squares, offering new insights into algebraic topology.

Findings

Clarified the structure of Peiffer pairings in bisimplicial groups

Connected Peiffer pairings to crossed modules and squares

Enhanced understanding of higher-dimensional algebraic structures

Abstract

In this work, we explain `Peiffer pairings' in the Moore (bi)complex of a bisimplicial group and give their applications for crossed modules and crossed squares.