Peiffer pairings in multisimplicial groups and crossed n-cubes and applications for bisimplicial groups

Abstract

We explore the Peiffer pairings within the Moore complex of multisimplicial groups, and as an application, we give a detailed construction of a crossed n- cube from an n-simplicial group in terms of these pairings. We also give explicit calculations of Peiffer pairings in the Moore bicomplex of a bisimplicial group to see the role of these pairings in the relationship between bisimplicial groups and crossed squares.