2013/01/16 by João Faria Martins, Martins, João Faria, Roger Picken +1 · 1 citation
Mathematics · #57M25 #57M27 (Primary) 18D10 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.AT #math.GT #math.QA #msc:18D10 #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.1301.3803
41 pages, 19 figures. This version 2 has minor corrections and additions, mainly in the references
arxiv created 2013/01/24 · arxiv updated 2013/01/28
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, 2-crossed modules and braided crossed modules. We prove that our construction includes all rack and quandle cohomology (framed) link invariants, as well as the Eisermann invariant of knots, for which we also find a lifting by using braided crossed modules.