Homology, Homotopy and Applications
Volume 16 (2014)
Crossed modules of racks
Pages: 85 – 106
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 rackspace 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.
crossed module of groups, rack, augmented rack, crossed module of racks, rack space, covering of rack space, link invariant, fundamental rack of a link, 2-group, 2-rack
2010 Mathematics Subject Classification
18B40, 18D05, 18D35, 20L05, 57M10, 57M25, 57Q45