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Home > JSJ decomposition

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

"Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible torii such that each component of the 3-manifold obtained by cutting along the tori is either atoroidal or Seifert-fibered "

See Thurston's conjecture for relevance.

The acronym JSJ is for Jaco, Shalen, and Johansson. The first two worked together, and the third worked independently.

External link

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

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JSJ decompositionGeometric topology The JSJ decomposition also known as the toral decomposition, is a topological construct given by the following theorem: "Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedd