Highly twisted diagrams
arXiv:2205.00703 · doi:10.2140/agt.2025.25.207
Abstract
We prove that the knots and links that admit a 3-highly twisted irreducible diagram with more than two twist regions are hyperbolic. This should be compared with a result of Futer-Purcell for 6-highly twisted diagrams. While their proof uses geometric methods our proof is achieved by showing that the complements of such knots or links are unannular and atoroidal. This is done by using a new approach involving an Euler characteristic argument.
38 pages, 45 figures