# nLab fundamental class

cohomology

## 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

(…)

Created on May 12, 2011 22:47:42 by Urs Schreiber (131.211.239.158)