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Simplicial Crossed Modules and Mapping Cones

Simplicial Crossed Modules and Mapping Cones Given a bisimplicial group 𝐺∗∗ such that 𝑁(𝐺)∗ 𝑞 = {1} for 𝑞 ⩾ 2, a simplicial group is obtained whose Moore complex is a mapping cone of the chain morphism 𝑁(𝐺)∗ 1 → 𝑁(𝐺)∗ 0 . This simplicial group is homotopy equivalent to the diagonal of 𝐺∗∗. In the last section a special case is considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Simplicial Crossed Modules and Mapping Cones

Georgian Mathematical Journal , Volume 10 (4) – Dec 1, 2003

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2003.623
Publisher site
See Article on Publisher Site

Abstract

Given a bisimplicial group 𝐺∗∗ such that 𝑁(𝐺)∗ 𝑞 = {1} for 𝑞 ⩾ 2, a simplicial group is obtained whose Moore complex is a mapping cone of the chain morphism 𝑁(𝐺)∗ 1 → 𝑁(𝐺)∗ 0 . This simplicial group is homotopy equivalent to the diagonal of 𝐺∗∗. In the last section a special case is considered.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2003

Keywords: Simplicial group; crossed module; mapping cone; generalized semi-direct product

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