Yu. Makhlin ^{1} and T. Misirpashaev ^{1,2}

*
^{1}Landau Institute for Theoretical Physics,
Kosygin St. 2, 117334 Moscow, Russia
^{2}Isaac Newton Institute for Mathematical Sciences, University of
Cambridge, Cambridge, CB3 OEH, U.K.
*

**Topology of vortex-soliton intersection: Invariants and
Torus homotopy**

JETP Lett. **61**, 49 (1995) [Pisma v ZhETF **61**, 48 (1995)]

The topology relevant to the intersection of nonsingular 4-pi vortex lines
with a planar transverse soliton in superfluid ^{3}He-A, which was
recently observed in Helsinki, is discussed. The essential part of the problem
consists in finding a homotopy classification of mappings ^{2}
x S^{1} -> S^{2}^{1} x
S^{1} x S^{1} -> S^{2}**v**_{s} curl **v**_{s}
dV/4k^{2}^{3} ->
S^{2}