Topology of vortex-soliton intersection: invariants and torus homotopy
Makhlin Yu.G., Misirpashaev T.Sh.
We discuss topology relevant to the intersection of nonsingular 4jr-vortex lines wxtb & planar transverse soli ton in superfluid -1He-A which was recently observed in Helsinki. The essential part of the problem consists in finding a ho mot ÏÒÕ classification of mappings 52 X 5l -ž S2 and S\ Χ 51 Χ 51 -» S2. This classification is achieved, and an analytical expression for the topological invariant is found, analogous to that for the Hopf invariant Η (1/4/c2) J v„ rotv„dV of mappings