Geodesic
Link invariants from finite categorical groups
Homology, homotopy, and applications, Tome 17 (2015) no. 2, pp. 205-233.

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

We define an invariant of tangles and framed tangles, given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks, quandles, rack and quandle cocycles, and central extensions of groups. We prove that our construction includes all rack and quandle cohomology (framed) link invariants, as well as the Eisermann invariant of knots. We construct a class of Reidemeister pairs which constitute a lifting of the Eisermann invariant, and show through an example that this class is strictly stronger than the Eisermann invariant itself.
DOI : 10.4310/HHA.2015.v17.n2.a11
Classification : 18D10, 57M25, 57M27
Keywords: knot invariant, tangle, peripheral system, quandle, rack, crossed module, categorical group, non-abelian tensor product of groups 
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     author = {Jo\~ao Faria Martins and Roger Picken},
     title = {Link invariants from finite categorical groups},
     journal = {Homology, homotopy, and applications},
     pages = {205--233},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2015},
     doi = {10.4310/HHA.2015.v17.n2.a11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2015.v17.n2.a11/}
}
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João Faria Martins; Roger Picken. Link invariants from finite categorical groups. Homology, homotopy, and applications, Tome 17 (2015) no. 2, pp. 205-233. doi : 10.4310/HHA.2015.v17.n2.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2015.v17.n2.a11/

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