Document Type
Article - post-print
Publication Date
2014
Abstract
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between crossed modules of groups and strict 2-groups. Then we explore topological applications. We show that by applying the rack-space functor, a crossed module of racks gives rise to a covering. Our main result shows how the fundamental racks associated to links upstairs and downstairs in a covering fit together to form a crossed module of racks.
Digital Commons @ LMU & LLS Citation
Crans, A. and Wagemann, F. “Crossed Modules of Racks.” Homology, Homotopy, and Applications, Vol. 16 (2014), No. 2: 85 – 106. Also available at http://arxiv.org/abs/1310.0852.
Comments
This is a post-print version of the article.