nLab
integral cohomology

Geometric models

Integral cohomology or “ordinary cohomology” (see there) 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 February 17, 2019 at 05:50:39. See the history of this page for a list of all contributions to it.