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

Authors

ÖZGÜN GÜRMEN ALANSAL
ERDAL ULUALAN

DOI

10.3906/mat-1912-75

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

First Page

360

Last Page

386

Recommended Citation

ALANSAL, ÖZGÜN GÜRMEN and ULUALAN, ERDAL (2021) "Peiffer pairings in multisimplicial groups and crossed $n$-cubes and applications for bisimplicial groups," Turkish Journal of Mathematics: Vol. 45: No. 1, Article 22. https://doi.org/10.3906/mat-1912-75
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/22