Jaco-Shalen-Johannson torus decomposition Guide, Meaning , Facts, Information and Description
The Jaco-Shalen-Johannson torus decomposition is a topological construct defined as follows:
"Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the 3-manifold removed by the tori is either atoroidal or Seifert-fibered"
See Thurston's conjecture for relevance.
External link
Allen Hatcher's Basic Topology of 3-Manifolds: http://www.math.cornell.edu/~hatcher/3M/3Mdownloads.html
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