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

Authors: ÖZGÜN GÜRMEN ALANSAL, ERDAL ULUALAN

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.

Keywords: Bisimplicial groups, crossed modules, crossed squares, crossed complexes

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