  Two different scenarios of the quantum critical point (QCP), a
zero-temperature instability of the Landau state, related to the divergence of
the effective mass, are investigated. Flaws of the standard scenario of the
QCP, where this divergence is attributed to the occurrence of some second-order
phase transition, are demonstrated. Salient features of a different {\it
topological} scenario of the QCP, associated with the emergence of bifurcation
points in equation $\epsilon(p)=\mu$ that ordinarily determines the Fermi
momentum, are analyzed. The topological scenario of the QCP is applied to
three-dimensional (3D) Fermi liquids with an attractive current-current
interaction.
