Generalized torsion elements in the knot groups of twist knots

Research paper by Masakazu Teragaito

Indexed on: 07 May '15Published on: 07 May '15Published in: Mathematics - Geometric Topology


It is well known that any knot group is torsion-free, but it may admit a generalized torsion element. We show that the knot group of any negative twist knot admits a generalized torsion element. This is a generalization of the same claim for the knot $5_2$, which is the $(-2)$-twist knot, by Naylor and Rolfsen.