Geodesic
Highly twisted diagrams
Lazarovich, Nir1 ; Moriah, Yoav1 ; Pinsky, Tali1
1Department of Mathematics, Technion, Haifa, Israel
Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 207-243
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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.

DOI : 10.2140/agt.2025.25.207
Keywords: knot diagrams, hyperbolic knots, twist regions, highly twisted diagrams, Euler characteristic

Lazarovich, Nir  1   ; Moriah, Yoav  1   ; Pinsky, Tali  1

1 Department of Mathematics, Technion, Haifa, Israel 
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Lazarovich, Nir; Moriah, Yoav; Pinsky, Tali. Highly twisted diagrams. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 207-243. doi: 10.2140/agt.2025.25.207

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