The Prevalence of Persistent Tangles

Louis H. Kauffman; Pedro Lopes

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arXiv · 1904.05951

The Prevalence of Persistent Tangles

Louis H. Kauffman·Pedro Lopes

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Abstract

This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be 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.

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Louis H. Kauffman, Pedro Lopes. 2019-04-11. The Prevalence of Persistent Tangles. https://arxiv.org/abs/1904.05951

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