A specious unlinking strategy
Stefan Friedl, Matthias Nagel, Mark Powell
TL;DR
This paper demonstrates that a common unlinking strategy, which involves minimal crossing changes followed by component unknotting, does not always produce an optimal sequence for unlinking links.
Contribution
It reveals the limitations of a widely used unlinking approach by providing counterexamples where it fails to be optimal.
Findings
The unlinking strategy is not universally optimal.
Counterexamples show the strategy's limitations.
Optimal unlinking sequences can differ significantly.
Abstract
We show that the following unlinking strategy does not always yield an optimal sequence of crossing changes: first split the link with the minimal number of crossing changes, and then unknot the resulting components.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Combinatorial Mathematics