Symmetric critical knots for O'Hara's energies

We prove the existence of symmetric critical torus knots for O'Hara's knot energy family Eα, α∈(2,3) using Palais' classic principle of symmetric criticality. It turns out that in every torus knot class there are at least two smooth Eα-critical knots, which supports experimental obser...

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Bibliographic Details
Published in:Topology and its applications 2018-06, Vol.242, p.73-102
Main Authors: Gilsbach, Alexandra, von der Mosel, Heiko
Format: Article
Language:English
Subjects:
Knot energy
Symmetric criticality
Torus knots
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Summary:We prove the existence of symmetric critical torus knots for O'Hara's knot energy family Eα, α∈(2,3) using Palais' classic principle of symmetric criticality. It turns out that in every torus knot class there are at least two smooth Eα-critical knots, which supports experimental observations using numerical gradient flows.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2018.04.014