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math.GT2025
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…
math.GT2025
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…