JSJ decomposition
From Academic Kids
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.
See the geometrization conjecture for relevance.
The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson. The first two worked together, and the third worked independently.
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See also
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External link
- Allen Hatcher, Notes on Basic 3-Manifold Topology (http://www.math.cornell.edu/~hatcher/3M/3Mdownloads.html).
