The prevalence of persistent tangles

Louis H. Kauffman, Pedro Lopes

Research output: Contribution to journalArticlepeer-review


This article addresses persistent tangles. These are tangles whose presence in a knot diagram implies the diagram is knotted. We provide new methods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main result in this article is that any knot admitting a non-trivial coloring gives rise to persistent tangles. Furthermore, we discuss when these persistent tangles are non-trivial.

Original languageEnglish
Article number107040
Number of pages12
JournalTopology and its Applications
Publication statusPublished - 15 Feb 2020


  • Colorings
  • Irreducible tangles
  • Knots
  • Persistent tangles
  • Tangles

Fingerprint Dive into the research topics of 'The prevalence of persistent tangles'. Together they form a unique fingerprint.

Cite this