3 papers
math.GT2026
The Forbidden Quiver of a Link
Sam Nelson, Stella Shah
The forbidden moves in virtual knot theory can be used to unknot any knot, virtual or classical; however, multi-component crossings in links can still survive, resulting a fused li…
math.GT2025
A Quick Note On Homsets and Diagrams
Sam Nelson
The homset invariant of a knot or link L with respect to an algebraic knot coloring structure X can be identified with a set of colorings of a diagram of L by elements of X via an…
math.GT2025
New Polynomial Decategorifications of the Quandle Coloring Quiver
Anusha Kabra, Sam Nelson
We introduce two new families of polynomial invariants of oriented classical and virtual knots and links defined as decategorfications of the quandle coloring quiver. We provide ex…