Geodesic
Crossed modules of racks
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 85-106.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2014.v16.n2.a5
Classification : 18B40, 18D05, 18D35, 20L05, 57M10, 57M25, 57Q45
Keywords: 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 
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     author = {Alissa S. Crans and Friedrich Wagemann},
     title = {Crossed modules of racks},
     journal = {Homology, homotopy, and applications},
     pages = {85--106},
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     number = {2},
     year = {2014},
     doi = {10.4310/HHA.2014.v16.n2.a5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a5/}
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Alissa S. Crans; Friedrich Wagemann. Crossed modules of racks. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 85-106. doi : 10.4310/HHA.2014.v16.n2.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a5/

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