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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.
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(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. …