I know that it is not possible to tie two knots in a one- dimensional string, such that the knots can untie each other. Are there objects analogous to knots in spaces with higher numbers of dimensions, which are stable alone but which can "untie" each other, or combine into a single simpler and topologically distinct object?
Edited 6/3/18: Please forgive any incorrect terminology; topology isn't my field of study. I'm asking this from a physics perspective. The idea that particles might be "knots" in the geometry of space isn't new, but I haven't found articles that address the idea of "knots and anti-knots", which might be a good model for particle - antiparticle creation and annihilation.
Antiparticles are very much like particles that have been reflected in the time axis, so pairs of objects that could make the analogy work would in some sense be reflections of each other. It might be that the kind of object needed might exist only in certain spaces with a complex metric, if it exists at all.
One helpful person (@ArnaudMortier) pointed out that braids can cancel each other out. That's easy to visualize and may turn out to be useful. However, the braids that come to mind require an already multiply connected substrate: a bundle of at least three long strands. I'm hoping that there might exist 3- or 4-dimensional sub-manifolds that can be created in pairs via a continuous deformation of a complex 4-manifold. Reversability of that process would allow for annihilation as well as creation of the pairs. End edit 6/3/18