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.

Articles in category "3-manifolds"

There are 27 articles in this category.

3-manifold A Atoroidal B Branched surface C Compression body Connected sum D Dehn surgery F Figure-eight knot (mathematics) G Geometrization conjecture H Haken manifold

H cont. Heegaard splitting Homology sphere Hyperbolic 3-manifold Hyperbolic link I Incompressible surface J JSJ decomposition L Lens space Lickorish-Wallace theorem P Poincaré conjecture Pretzel link

P cont. Property P conjecture S Scott core theorem Seifert-Weber space Spherical 3-manifold Sufficiently large T Taut foliation Thurston elliptization conjecture Torus bundle