We present the notion of a Heegaard splitting of a closed manifold, which is defined as a decomposition into two handlebodies. A common proof of its existence follows the manifold's triangulability property and a theorem by Moise. Instead, we prove it using Morse theory. We take a look at Morse's lemma, fundamental theorems of Morse theory and their corollaries, which we then use in construction of a function that explicitly gives the Heegaard splitting. Lastly, we find such a splitting of a 3-dimensional torus.
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