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A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.

18 votes

(Very) High dimensional manifolds

An important property of the cohomology of manifolds is the formality, which has been at the heart of a lot of work in rational homotopy theory. … simply connected manifolds (Fernandez-Munoz) for instance. …