From the 1 of 6 linked papers with an AI index.
6 papers
A note on longitudes of virtual knots
Lorenzo Traldi, Daniel S. Silver
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.
Peripheral structures of core groups
Daniel S. Silver, Lorenzo Traldi
The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show t…
Reorienting quandle orbits
Lorenzo Traldi
Motivated by knot theory, it is natural to define the orientation-reversal of a quandle orbit by inverting all the translations given by elements of that orbit. In this short note…
Multivariate Alexander quandles, VI. Metabelian groups and 2-component links
Lorenzo Traldi
We prove two properties of the modules and quandles discussed in this series. First, the fundamental multivariate Alexander quandle is isomorphic to the natural image of t…
Peripheral elements in reduced Alexander modules: an addendum
Daniel S. Silver, Lorenzo Traldi
We answer a question raised in ``Peripheral elements in reduced Alexander modules'' [J. Knot Theory Ramifications 31 (2022), 2250058]. We also correct a minor error in that paper.
Core groups
Daniel S. Silver, Lorenzo Traldi, Susan G. Williams
The core group of a classical link was introduced independently by A.J. Kelly in 1991 and M. Wada in 1992. It is a link invariant defined by a presentation involving the arcs and c…