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1. Smooth Manifold

   Linked via "cotangent bundle"

   De Rham Cohomology and Global Properties
   Smooth manifolds possess global topological invariants derived from their calculus structures. The de Rham cohomology groups $H_{\text{dR}}^k(M)$ utilize differential forms, which are smooth sections of the cotangent bundle $T^*M$.
   The exterior derivative $d$ acts on $k$-forms, and the cohomology is defined by: