A note on longitudes of virtual knots
arXiv:2607.27425
summary
The paper shows that for virtual knots, the longitude element also lies in the second commutator subgroup of the knot group, extending a known property from classical knots.
Abstract
It is a famous property that a longitude of a classical knot lies in the second commutator subgroup of the knot group. We observe that the same property holds for a longitude of a virtual knot.
5 pages, 1 figure
Topics & keywords
#virtual knots#knot groups#longitudes#commutator subgroups#algebraic topologylongitudevirtual knotknot groupsecond commutator subgroupgroup theory