Simplifying Weinstein Morse functions

Abstract

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. As a corollary, we obtain a topological upper bound on the number of generators of the wrapped Fukaya category of the domain. We also show that there is an upper bound on the number of gradient trajectories between critical points in smoothly trivial Weinstein cobordisms.