Large volume fibred knots of fixed genus
Kenneth L. Baker, David Futer, Jessica S. Purcell, Saul Schleimer
TL;DR
This paper demonstrates that for hyperbolic fibred knots in the three-sphere, volume, genus, strong quasipositivity, and Seifert form are independent properties, challenging previous assumptions about their relationships.
Contribution
It establishes the independence of volume from genus, strong quasipositivity, and Seifert form in hyperbolic fibred knots, providing new insights into their geometric and topological properties.
Findings
Volume is unrelated to genus in hyperbolic fibred knots.
Volume is unrelated to strong quasipositivity.
Volume is unrelated to Seifert form.
Abstract
We show that, for hyperbolic fibred knots in the three-sphere, the volume and the genus are unrelated. Furthermore, for such knots, the volume is unrelated to strong quasipositivity and Seifert form.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows