Ravels arising from Montesinos Tangles

TL;DR

This paper characterizes when Montesinos tangles can be transformed into ravels, which are non-planar spatial graphs without non-trivial knots or links, through vertex closure and crossing replacements.

Contribution

It provides a complete characterization of conditions under which Montesinos tangles can become ravels via specific closure and crossing modifications.

Findings

Identifies conditions for Montesinos tangles to become ravels.

Describes effects of crossing replacements on tangle topology.

Provides criteria for ravel formation from Montesinos tangles.

Abstract

A ravel is a spatial graph which is non-planar but contains no non-trivial knots or links. We characterize when a Montesinos tangle can become a ravel as the result of vertex closure with and without replacing some number of crossings by vertices.