Virtual Tribrackets
Sam Nelson, Shane Pico
TL;DR
This paper introduces virtual tribrackets, a new algebraic structure for coloring regions in virtual knot diagrams, enabling the definition of invariants that can distinguish certain virtual knots.
Contribution
The paper presents the concept of virtual tribrackets and demonstrates their use in defining and computing invariants for virtual knots and links, which can distinguish specific virtual knots.
Findings
Virtual tribrackets can distinguish certain virtual knots.
The invariants are computable from the virtual knot diagrams.
Examples illustrate the effectiveness of the invariants.
Abstract
We introduce virtual tribrackets, an algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram. We use these structures to define counting invariants of virtual knots and links and provide examples of the computation of the invariant; in particular we show that the invariant can distinguish certain virtual knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Computational Geometry and Mesh Generation