nLab
integral cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

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Integral cohomology or “ordinary cohomology” is the ordinary version of generalized (Eilenberg-Steenrod) cohomology, the one that is represented by the Eilenberg-MacLane spectrum.

Integral cohomology is best known maybe in its incarnation as singular cohomology or Čech cohomology with coefficients in the integers.

Geometric models

  • integral cohomology in degree 1 classifies complex line bundle;

  • integral cohomology in degree 2 classifies complex line bundle gerbe / line 2-bundles;

  • integral cohomology in degree nn classifies line n-bundles .

Last revised on December 19, 2009 at 03:21:02. See the history of this page for a list of all contributions to it.