Highly twisted diagrams

Lazarovich, Nir; Moriah, Yoav; Pinsky, Tali

doi:10.2140/agt.2025.25.207

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Highly twisted diagrams

Nir Lazarovich, Yoav Moriah and Tali Pinsky

Algebraic & Geometric Topology 25 (2025) 207–243

DOI: 10.2140/agt.2025.25.207

Abstract

We prove that knots and links that have a $3$ -highly twisted irreducible diagram with more than two twist regions are hyperbolic. Furthermore, this result is sharp. The result is obtained using combinatorial techniques, using a new approach involving the Euler characteristic. By using geometric techniques, Futer and Purcell proved hyperbolicity under the assumption that the diagram is $6$ -highly twisted.

Keywords

knot diagrams, hyperbolic knots, twist regions, highly twisted diagrams, Euler characteristic

Mathematical Subject Classification

Primary: 57K10, 57K32, 57K99

References

Publication

Received: 6 September 2022

Revised: 23 July 2023

Accepted: 7 September 2023

Published: 5 March 2025

Authors

Nir Lazarovich
Department of Mathematics Technion Haifa Israel

Yoav Moriah
Department of Mathematics Technion Haifa Israel

Tali Pinsky
Department of Mathematics Technion Haifa Israel

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 1 (2025)