Morse Theory
A 3-manifold is a space that locally resembles Euclidean 3-dimensional space. More specifically, every point in a 3-manifold has a neighborhood that is homeomorphic to an open subset of $$\mathbb{R}^3$$. Understanding 3-manifolds is crucial because they form the basis for many geometric and topological structures, including handlebodies, which are essential in constructing complex shapes and analyzing their properties.
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