Fundamental class

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In mathematics, the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of the homology group ${\displaystyle H_{n}(M,\partial M;\mathbf {Z} )\cong \mathbf {Z} }$ . The fundamental class can be thought of as the orientation of the top-dimensional simplices of a suitable triangulation of the manifold.