Ottesen's conjecture

Ottesen's conjecture relates to knot theory, specifically the behavior of certain knots called hyperbolic knots. It suggests that if a hyperbolic knot has a large enough volume (a measurement of its geometric complexity), then it should contain certain simple building blocks called essential surfaces. In essence, the conjecture predicts a connection between the geometric size of a knot and its internal structure, implying that more complex knots (with bigger volumes) have richer, more intricate internal surfaces. This idea aims to deepen understanding of how the shape and size of knots influence their topological properties.