2021/10/11 by Dye, Heather A., Kaestner, Aaron
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2110.05613
For a knot diagram K, the classical knot group π1(K) is a free group modulo relations determined by Wirtinger-type relations on the classical crossings. The classical knot group is invariant under the Reidemeister moves. In this paper, we define a set of quotient groups associated to a knot diagram K. These quotient groups are invariant under the Reidemeister moves and the set includes the extended knot groups defined by Boden et al and Silver and Williams.