Morse-Smale complex
= Morse-Smale complex
{c}
{title2=$\partial p=\sum_{\operatorname{ind}q=\operatorname{ind}p-1}n(p,q)q$}
Here $n(p,q)$ is the signed number of unparametrized trajectories of a <Morse-Smale gradient flow> from $p$ to $q$. Compactifying one-dimensional trajectory moduli spaces gives $\partial^2=0$. The generators coincide with the cells furnished by the <unstable manifolds>, and the trajectory count is their cellular incidence number, so the complex computes integral <homology>.