Peiffer Pairings in Multisimplicial Groups and Crossed n-cubes and Applications for Bisimplicial Groups

2020 Turkish Journal of Mathematics  
We explore the Peiffer pairings within the Moore complex of multisimplicial groups, and as an application, 5 we give a detailed construction of a crossed n -cube from an n -simplicial group in terms of these pairings. We also give 6 explicit calculations of Peiffer pairings in the Moore bicomplex of a bisimplicial group to see the role of these pairings in 7 the relationship between bisimplicial groups and crossed squares. 8
doi:10.3906/mat-1912-75 fatcat:4xkwrked65duvoalgagbxvv4pe