  Let $Crit M$ denote the minimal number of critical points (not necessarily
non-degenerate) on a closed smooth manifold $M$. We are interested in the
evaluation of $Crit$. It is worth noting that we do not know yet whether $Crit
M$ is a homotopy invariant of $M$. This makes the research of $Crit$ a
challenging problem.
  In particular, we pose the following question: given a map $f: M \to N$ of
degree 1 of closed manifolds, is it true that $Crit M \geq Crit N$? We prove
that this holds in dimension 3 or less. Some high dimension examples are
considered. Note also that an affirmative answer to the question implies the
homotopy invariance of $Crit$; this simple observation is a good motivation for
the research.
