Editing Geometric topology (section)

===Fundamental group===
{{main|Fundamental group}}
In all dimensions, the [[fundamental group]] of a manifold is a very important invariant, and determines much of the structure; in dimensions 1, 2 and 3, the possible fundamental groups are restricted, while in dimension 4 and above every [[finitely presented group]] is the fundamental group of a manifold (note that it is sufficient to show this for 4- and 5-dimensional manifolds, and then to take products with spheres to get higher ones).