Knot theory, a branch of topology dedicated to the study of embeddings of circles in three-dimensional space, intersects deeply with homotopy theory—the study of continuous deformations between ...

(Nanowerk News) Consider a short piece of rope: could you guess which knots are more likely to form if you crumple and shake it? Synthetic chemists have long been working on a molecular version of ...

Many of the processes essential to life involve proteins -- long molecules which 'fold' into three-dimensional shapes allowing them to perform their biological role. Many of the processes essential to ...

Knots are everywhere—from tangled headphones to DNA strands packed inside viruses—but how an isolated filament can knot itself without collisions or external agitation has remained a longstanding ...

Knots are used in all sorts of ways, every day. They ensure safety both indoors and for outdoor activities such as boating or sailing, are used as surgical sutures, as decorations, and they can even ...