High Quality Content by WIKIPEDIA articles! In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Some examples of topics in geometric topology are orientability, handle decompositions, local flatness, and the planar and higher-dimensional Schonflies theorems. 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 every 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).

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