  We prove that the minimum number of critical points of a Weinstein Morse
function on a Weinstein domain of dimension at least six is at most two more
than the minimum number of critical points of a smooth Morse function on that
domain; if the domain has non-zero middle-dimensional homology, these two
numbers agree. There is also an upper bound on the number of gradient
trajectories between critical points in smoothly trivial Weinstein cobordisms.
As an application, we show that the number of generators for the Grothendieck
group of the wrapped Fukaya category is at most the number of generators for
singular cohomology and hence vanishes for any Weinstein ball. We also give a
topological obstruction to the existence of finite-dimensional representations
of the Chekanov-Eliashberg DGA of Legendrian spheres.
