nLab fundamental class

Definition

For manifolds

For $X$ a connected oriented closed manifold, its integral homology group in degree the dimension of $X$ is isomorphic to the integers

${H}_{\mathrm{dim}X}\left(X,ℤ\right)\simeq ℤ\phantom{\rule{thinmathspace}{0ex}}.$H_{dim X}(X, \mathbb{Z}) \simeq \mathbb{Z} \,.

The generator of this corresponding to the choice of orientation is called the fundamental class of $X$.

Virtual fundamental class

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Revised on July 19, 2013 15:48:13 by Urs Schreiber (89.204.138.251)