6 papers
Polynomial Link Invariants via Decategorification of Subquandle Quiver Filtrations
Jose Ceniceros, Benjamin Chidley, Jackson Vaughn
In this paper, we introduce the notion of subquandle filtrations for finite quandles as a foundation to construct algebraic and combinatorial link invariants. A nested sequence of…
Virtual Biquandle Cocycle Quiver Representations
Alexander Bishop, Jose Ceniceros, Sam Nelson
We introduce quiver representation-valued invariants of oriented virtual knots and links associated to a choice of finite virtual biquandle, abelian group, set of virtual Boltzmann…
Pointed Quandle Coloring Quivers of Linkoids
Jose Ceniceros, Max Klivans
We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynom…
Pointed Racks and Their Applications to Braid Theory
Angel Apollos, Jose Ceniceros
We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of -braids. We first introduce an integer-valued invariant…
Generalized Quandle Polynomials and Their Applications to Stuquandles, Stuck Links, and RNA Folding
Ekaterina Bondarenko, Jose Ceniceros, Mohamed Elhamdadi +1
We introduce a generalization of the quandle polynomial. We prove that our polynomial is an invariant of stuquandles. Furthermore, we use the invariant of stuquandles to define a p…
-Fold Cyclic Branched Covers and Overtwisted Contact Structures
Jose Ceniceros
This article presents an alternate way to prove a result originally proven by Harvey, Kawamuro, and Plamenvskaya in \cite{HaKaPl}. We accomplish this by explicitly constructing an…