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 ...

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 this problem and, ...

(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 ...

Can the topology of microobjects influence the way they move in a fluid? Experiments and simulations of Polish and Swiss researchers published in the Physical Review Letters show that the dynamics of ...

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 ...

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 ...

Like a scouting handbook for the molecular realm, a new chart reveals how to tie molecules up in knots of increasing complexity. Mathematicians have cataloged billions of distinct knot types, but ...