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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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Preimage of $1 \in H^n(M^n)$ under Chern character

In algebraic geometry setting, this would be a structure sheaf of a point (or if you wish a linear combination of the vector bundles that provide projective resolution of such sheaf).
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