Lectures on Morse homology

About this book

A Morse-Smale function f : M R on a finite dimensional compact smooth Riemannian manifold (M, g) gives rise to a chain complex (C*(f), *), called the Morse-Smale-Witten chain complex (Definition 7.2), whose chains are generated by the critical points of f and whose boundary operator is defined by counting gradient flow lines (with sign).