Morse Theory
Orientation in the context of differential forms on manifolds refers to a consistent choice of 'direction' throughout a manifold, allowing for the meaningful integration of differential forms. This concept is essential because it establishes how we can define and distinguish between forms in different parts of the manifold, impacting how we compute integrals and analyze geometric properties. Orientation helps in understanding topological features of manifolds, influencing notions like homology and cohomology.
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