Low-dimensional topology

A three-dimensional depiction of a thickened trefoil knot, the simplest non-trivial knot. Knot theory is an important part of low-dimensional topology.

In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of continuum theory.