Crossed modules of racks
Preprint, Other literature type
Crans, Alissa S.
- Publisher: International Press of Boston
rack | link invariant | 2-group | Crossed module of groups | augmented rack | rack space | 20L05 | 57M25 | 18D05 | 57M10 | 18D35 | crossed module of racks | 2-rack | 57Q45 | 18B40, 18D05, 18D35, 20L05, 57M10, 57M25, 57Q45 | 18B40 | fundamental rack of a link | Mathematics - Quantum Algebra | covering of rack space
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.