Hyperbolic geometry of multiply twisted knots
Jessica S. Purcell
TL;DR
This paper explores the hyperbolic geometry of multiply twisted knots and links, providing insights into their volume and geodesic structures based solely on diagrammatic analysis.
Contribution
It introduces a method to determine geometric properties of these knots from diagrams using generalized augmentations.
Findings
Volume estimates for multiply twisted knots
Identification of isotopy classes of geodesics
Diagram-based geometric information extraction
Abstract
We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based only on a diagram. The results are obtained by finding geometric information on generalized augmentations of these links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows