cohomology

# Contents

## 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

$H_{dim X}(X, \mathbb{Z}) \simeq \mathbb{Z} \,.$

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 May 31, 2014 07:25:49 by Urs Schreiber (89.204.135.200)