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.
- Irreducible tangles
- Persistent tangles