Whitehead Link

The Whitehead link is a link of two interlocked closed loops that has a linking number of zero, meaning the simplest algebraic measure of how the two loops wind around each other reports no linkage at all, even though the two loops genuinely cannot be pulled apart without cutting one of them. It is named after the British mathematician J. H. C. Whitehead, who discovered it in 1934 while investigating a question in the topology of three dimensional space closely tied to Henri Poincare's conjecture, making the link an early and influential counterexample to any assumption that linking number alone detects whether two loops are truly linked. Drawn in its simplest diagram the Whitehead link has five crossings, and it is chiral, meaning its mirror image is not the same as the original link no matter how it is rotated in space. The link and the technique used to construct it, whitehead doubling, remain standard tools in low dimensional topology and knot theory.