TL;DR
This paper introduces a method to distinguish certain knot-like objects by analyzing equivalence classes under only 2nd Reidemeister moves, simplifying the recognition of non-equivalence.
Contribution
It presents a novel approach to recognize non-equivalence of knot-like objects using equivalence classes modulo only 2nd Reidemeister moves, with applications to virtual knots and related structures.
Findings
Non-equivalence can be recognized via 2nd Reidemeister move classes
Applicable to virtual knots, graph-links, and looped graphs
Simplifies knot equivalence recognition process
Abstract
We prove that for some knot-like objects one can easily recognize non-equivalence w.r.t. all Reidemeister moves by studying some equivalence classes modulo only 2nd Reidemeister moves. There are applications to virtual knots, graph-links and looped graphs.
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Taxonomy
TopicsGeometric and Algebraic Topology · Artificial Intelligence in Games · Mathematical Dynamics and Fractals