Highly twisted diagrams

Nir Lazarovich; Yoav Moriah; Tali Pinsky

doi:10.2140/agt.2025.25.207

Highly twisted diagrams

Nir Lazarovich, Yoav Moriah, Tali Pinsky

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	207-243
Number of pages	37
Journal	Algebraic and Geometric Topology
Volume	25
Issue number	1
DOIs	https://doi.org/10.2140/agt.2025.25.207
State	Published - 2025

Keywords

Euler characteristic
highly twisted diagrams
hyperbolic knots
knot diagrams
twist regions

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/agt.2025.25.207

Cite this

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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.",

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AU - Moriah, Yoav

AU - Pinsky, Tali

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KW - highly twisted diagrams

KW - hyperbolic knots

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KW - twist regions

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Highly twisted diagrams

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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