Homology, Homotopy and Applications
Volume 17 (2015)
Link invariants from finite categorical groups
Pages: 205 – 233
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.
knot invariant, tangle, peripheral system, quandle, rack, crossed module, categorical group, non-abelian tensor product of groups
2010 Mathematics Subject Classification
18D10, 57M25, 57M27