nLab
fundamental class

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Definition

For manifolds

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

H dimX(X,). 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 XX.

Virtual fundamental class

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