The Morse number 
of a closed smooth manifold 
is the minimum number of critical
points among its Morse functions. Every critical point in the defining minimum
is nondegenerate. Distinct critical values can be arranged without changing their
number. The Morse inequalities give lower bounds
from the Betti numbers, but these bounds need not
attain the Morse number. For a positive-dimensional
sphere, a height function
has two critical points, so its Morse number is
2. The stable Morse number permits auxiliary
variables and can differ from this invariant.
Morse Number
See also
Arnold Conjecture, Morse Function, Morse Inequalities, Morse Theory, Stable Morse NumberExplore with Wolfram|Alpha
References
Cannas da Silva, A. Lectures on Symplectic Geometry. Berlin: Springer-Verlag, 2001. https://people.math.ethz.ch/~acannas/Papers/lsg.pdf.Cite this as:
Weisstein, Eric W. "Morse Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MorseNumber.html