The fundamental class in cohomology is an essential concept that represents a top-dimensional cycle of a manifold in a cohomology group. It provides a way to associate algebraic invariants with geometric objects, linking the manifold's topology to its algebraic structure. This class serves as a cornerstone for the development of cohomological theories and is crucial for understanding Poincaré duality, as it allows one to capture the manifold's intrinsic properties in a cohomological framework.
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