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The topological superfluid 3He-B provides many examples of the interplay ofsymmetry and topology. Here we consider the effect of magnetic field ontopological properties of 3He-B. Magnetic field violates the time reversalsymmetry. As a result, the topological invariant supported by this symmetryceases to exist; and thus the gapless fermions on the surface of 3He-B are notprotected any more by topology: they become fully gapped. Nevertheless, ifperturbation of symmetry is small, the surface fermions remain relativisticwith mass proportional to symmetry violating perturbation -- magnetic field.The 3He-B symmetry gives rise to the Ising variable I=+/- 1, which emerges inmagnetic field and which characterizes the states of the surface of 3He-B. Thisvariable also determines the sign of the mass term of surface fermions and thetopological invariant describing their effective Hamiltonian. The line on thesurface, which separates the surface domains with different I, contains 1+1gapless fermions, which are protected by combined action of symmetry andtopology.

Topological superfluid 3He-B in magnetic field and Ising variable