Biquandle longitude invariant of long virtual knots
Maciej Niebrzydowski (University of Louisiana at Lafayette)
TL;DR
This paper introduces a new biquandle-based invariant for long virtual knots, extending the classical coloring invariant by incorporating longitudinal information through biquandle endomorphisms.
Contribution
It develops a novel family of biquandle endomorphisms derived from colorings and longitudinal data, providing a more refined invariant for long virtual knots.
Findings
The invariant distinguishes certain long virtual knots that previous invariants could not.
The method generalizes existing biquandle coloring invariants by adding longitudinal structure.
It offers a new tool for knot classification and study in virtual knot theory.
Abstract
It is known that the number of biquandle colorings of a long virtual knot diagram, with a fixed color of the initial arc, is a knot invariant. In this paper we describe a more subtle invariant: a family of biquandle endomorphisms obtained from the set of colorings and longitudinal information.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics