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Once a small subfield of geometric topology, the theory of 3-manifolds has experienced tremendous growth in the latter half of the 20th century. The methods used tend to be quite specific to three dimensions, since different phenomena occur for 4-manifolds and higher dimensions.

See the main article on 3-manifolds for details on basic background, important theorems and conjectures, and connections to other fields. Category:Knot theory may also be of interest because of the substantial overlap in content.