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Article Dans Une Revue Homology, Homotopy and Applications(HHA) Année : 2014

Crossed modules of racks

Résumé

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.

Dates et versions

hal-00874550 , version 1 (18-10-2013)

Identifiants

Citer

Alissa S. Crans, Friedrich Wagemann. Crossed modules of racks. Homology, Homotopy and Applications(HHA), 2014, 16 (2), pp.85-106. ⟨10.4310/HHA.2014.v16.n2.a5⟩. ⟨hal-00874550⟩
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