Configurations in Crystals, Rod Lattices, and Lamellar Systems
Hans‐Rainer Trebin · Physical Review Letters · 1983
For three-dimensional ordered media of periodic and partially periodic structure, homotopy theory allows the existence of nonsingular stable distortion fields, which are finite in size and thus resemble extended particles. It is shown that because of integrability conditions homotopy arguments are not adequate for these systems. By methods of differential topology it is proved that in three dimensions topological particles of this type are unstable, but that there are analogous fields in higher dimensions that cannot decay to a uniform ground state.