The Montesinos trick for proper rational tangle replacement
Geometric Topology
2021-10-29 v1
Abstract
Recently Iltgen, Lewark and Marino introduced the concept of a proper rational tangle replacement and the corresponding notion of the proper rational unknotting number. In this note we derive a version of the Montesinos trick for proper rational tangle replacement and use it to study knots with proper rational unknotting number one. We prove that knots with proper rational unknotting number one are prime and classify the alternating knots with proper rational unknotting number one. We also study Montesinos knots with proper rational unknotting number one.
Cite
@article{arxiv.2110.15106,
title = {The Montesinos trick for proper rational tangle replacement},
author = {Duncan McCoy and Raphael Zentner},
journal= {arXiv preprint arXiv:2110.15106},
year = {2021}
}
Comments
12 pages, 9 figures