# First cohomology group with integer coefficients

From Topospaces

## Definition

Let be a path-connected space). The **first cohomology group with integer coefficients** of , denoted or is defined in the following equivalent ways:

- It is the set of homotopy classes of based maps from to
- It is the set of homotopy classes of unbased maps from to
- It is the set of fiber bundles over with fiber equal to (in other words, it is the covering spaces (possible disconnected) whose fibers are the group )