ﻻ يوجد ملخص باللغة العربية
We generalize the notion of the quandle polynomial to the case of singquandles. We show that the singquandle polynomial is an invariant of finite singquandles. We also construct a singular link invariant from the singquandle polynomial and show that this new singular link invariant generalizes the singquandle counting invariant. In particular, using the new polynomial invariant, we can distinguish singular links with the same singquandle counting invariant.
We introduce algebraic structures known as psybrackets and use them to define invariants of pseudoknots and singular knots and links. Psybrackets are Niebrzydowski tribrackets with additional structure inspired by the Reidemeister moves for pseudokno
We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called emph{oriented singquandles} and assigning weight functions at both regular and singular crossings. This invariant coincides with the classi
Kashaev and Reshetikhin previously described a way to define holonomy invariants of knots using quantum $mathfrak{sl}_2$ at a root of unity. These are generalized quantum invariants depend both on a knot $K$ and a representation of the fundamental gr
Let $G$ be a nonabelian, simple group with a nontrivial conjugacy class $C subseteq G$. Let $K$ be a diagram of an oriented knot in $S^3$, thought of as computational input. We show that for each such $G$ and $C$, the problem of counting homomorphism
We introduce shadow structures for singular knot theory. Precisely, we define emph{two} invariants of singular knots and links. First, we introduce a notion of action of a singquandle on a set to define a shadow counting invariant of singular links w