Translator Disclaimer
September 2021 Tangle decompositions of alternating link complements
Joel Hass, Abigail Thompson, Anastasiia Tsvietkova
Author Affiliations +
Illinois J. Math. 65(3): 533-545 (September 2021). DOI: 10.1215/00192082-9291846

Abstract

Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish; Lickorish proved that by summing prime tangles one obtains a prime link. In a similar spirit, summing two prime alternating tangles will produce a prime alternating link if summed correctly with respect to the alternating property. Given a prime alternating link, we seek to understand whether it can be decomposed into two prime tangles, each of which is alternating. We refine results of Menasco and Thistlethwaite to show that if such a decomposition exists, either it is visible in an alternating link diagram or the link is of a particular form, which we call a pseudo-Montesinos link.

Citation

Download Citation

Joel Hass. Abigail Thompson. Anastasiia Tsvietkova. "Tangle decompositions of alternating link complements." Illinois J. Math. 65 (3) 533 - 545, September 2021. https://doi.org/10.1215/00192082-9291846

Information

Received: 10 December 2019; Revised: 28 March 2021; Published: September 2021
First available in Project Euclid: 7 July 2021

Digital Object Identifier: 10.1215/00192082-9291846

Subjects:
Primary: 57M35

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.65 • No. 3 • September 2021
Back to Top