The Cochran–Harvey–Leidy fractal conjecture for knot concordance groups

Let $\mathcal{C}^\mathrm{diff}$ and $\mathcal{C}^\mathrm{top}$ denote the smooth and topological knot concordance groups. A set has a fractal structure if it admits self-similarities at arbitrarily small scales. Cochran–Harvey–Leidy fractal conjecture. The knot concordance groups have the structure of a fractal. Injective satellite operators and robust doubling operators provide evidence for such self-similarities, but a suitable metric and a complete understanding of the structure remain open.