AV Vologodskii

B Fuller

CE Laing

D Kleckner

D Proment

DeW Sumners

DI Pontin

F Maggioni

G Bewley

HK Moffatt

K Shimokawa

NJ Crisona

RL Ricca

S Kida

S Lugomer

S Zuccher

W van Rees

WBR Lickorish

X Liu

Scientific Reports

AbstractDue to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.</jats:p

Xin Liu

Renzo L. Ricca

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Knots cascade detected by a monotonically decreasing sequence of values

Knots cascade detected by a monotonically decreasing sequence of values

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