Equivariant isotopy of unknots to round circles

Michael H. Freedman, Feng Luo

Research output: Contribution to journalArticlepeer-review


Suppose that γ0 is an unknotted simple closed curve contained in the 3-sphere which happens to be invariant under a subgroup G of the Möbius group of S3 = the group (generated by inversions in 2-spheres). It is shown that there is an equivariant isotopy γt, 0 ≤ t ≤ 1, from γ0 to a round circle γ1.

Original languageEnglish
Pages (from-to)59-74
Number of pages16
JournalTopology and its Applications
Issue number1
StatePublished - 16 Jun 1995
Externally publishedYes


  • Knot
  • Möbius energy
  • Möbius group
  • Unknotting

ASJC Scopus subject areas

  • Geometry and Topology


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