Contents

cohomology

# Contents

## Idea

Integral cohomology or “ordinary cohomology” (see there) is the ordinary version of Whitehead-generalized cohomology, the one that is represented by the Eilenberg-MacLane spectrum $H \mathbb{Z}$ with coefficients in the integers.

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 $n$ classifies line n-bundles.

## References

Discussion in homotopy type theory:

Last revised on June 15, 2022 at 13:13:50. See the history of this page for a list of all contributions to it.