  We discuss topological properties of the ground state of spatially
homogeneous ensemble of fermions. There are several classes of topologically
different fermionic vacua; in each case the momentum space topology of the
vacuum determines the low-energy (infrared) properties of the fermionic energy
spectrum. Among them there is a class of the gapless systems which is
characterized by the Fermi-hypersurface, which is the topologically stable
singularity in momentum space. This class contains the conventional Landau
Fermi-liquid and also the non-Landau Luttinger Fermi-liquid. Another important
class of gapless systems is characterized by the topologically stable point
nodes (Fermi points). Superfluid 3He-A and electroweak vacuum belong to this
universality class. The fermionic quasiparticles (particles) in this class are
chiral: close to the Fermi points they are left-handed or right-handed massless
relativistic particles. Since the spectrum becomes relativistic at low energy,
the symmetry of the system is enhanced in the low-energy edge. The low-energy
dynamics acquires local invariance, Lorentz invariance and general covariance,
which become better and better when the energy decreases. Interaction of the
fermions near the Fermi point leads to collective bosonic modes, which look
like effective gauge and gravitational fields. Since the vacuum of superfluid
3He-A and electroweak vacuum are topologically similar, we can use 3He-A for
simulation of many phenomena in high energy physics, including axial anomaly.
3He-A textures induce a nontrivial effective metrics of the space, where the
free quasiparticles move along geodesics. Possible simulation in 3He-A of event
horizon, Hawking radiation, rotating vacuum and conical space are discussed.
