The paper constructs a Gordian pair of links: two configurations that both minimize total ropelength in their link homotopy class, yet no length-preserving thick homotopy connects them.
Gordian Unknots
1 Pith paper cite this work. Polarity classification is still indexing.
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Pith paper citing it
abstract
Numerical simulations indicate that there exist conformations of the unknot, tied on a finite piece of rope, entangled in such a manner, that they cannot be disentangled to the torus conformation without cutting the rope. The simplest example of such a gordian unknot is presented.
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2019 1verdicts
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A Gordian Pair of Links
The paper constructs a Gordian pair of links: two configurations that both minimize total ropelength in their link homotopy class, yet no length-preserving thick homotopy connects them.