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, ...

Recently it has been proved that if and only if two knots K1 and K2 have the same value for the Vassiliev invariant of type two, then K1 can be deformed into K2 by a finite sequence of clasp-pass ...

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 ...