A formal manifold is a concept from the field of mathematics, particularly in differential geometry and algebraic geometry. It is primarily used in the study of smooth manifolds and formal schemes. In essence, a formal manifold is a "manifold" that is equipped with a formal structure allowing for the study of its infinitesimal properties without relying on the usual notions of topology or smoothness. Instead, it utilizes a local coordinate system that behaves much like a formal power series.
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