Topology of vortex-soliton intersection: Invariants and Torus homotopy
Makhlin Yu. G. , Misirpashaev T. Sh.
The topology relevant to the intersection of nonsingular 4π vortex lines with a planar transverse soliton in superfluid 3He-A, which was recently observed in Helsinki, is discussed. The essential part of the problem consists in finding a homotopy classification of mappings 52XS'->52 and 51X51X51->52. This classification is achieved, and an analytical expression for the topological invariant is found. This expression is analogous to that for the Hopf invariant Η=(l/4A<2)/vJcurl \sgV of mappings S3—>S2. © 1995 American Institute of Physics.