Homología de Morse en variedades compactas

Given a compact Riemannian manifold $(M g)$ and Morse function $f:m\to \mathbb{R}$ whose gradient flow satisfies the Morse-Smale condition, (i.e. the stable and unstable manifolds of f intersect transversely) we construct a chain complex called the Morse-Witten Complex. Our goal on this paper is show that the homology of the Morse-Witten complex is isomorphic to the singular homology of $M$.

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