JSJ decomposition

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In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem:

Irreducible orientable compact and closed (i.e., without boundary) 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the 3-manifold obtained by cutting along the tori is either atoroidal or Seifert-fibered.

The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson. The first two worked together, and the third worked independently.

See also

• Geometrization conjecture
• Manifold decomposition

External link

• Allen Hatcher, Notes on Basic 3-Manifold Topology.