A recent paper makes a connection between the quantum group SLq(2), which describes knots, and the elementary particles of the Standard Model. A mathematical knot is an embedding of a circle in 3-dimensional Euclidean space. Unlike your shoes, with their knot
the ends are joined together so it cannot be undone. The Standard Model, created in the 1970s, is the dominant hypothesis concerning electromagnetic, weak, and strong nuclear interactions in fundamental particles.
Some suggest that leptons, neutrinos, and quarks might be composite and the authors seeks to make the case that the structure is described by the quantum group SLq(2).