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.
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.
See also
External link
- Allen Hatcher, Notes on Basic 3-Manifold Topology (http://www.math.cornell.edu/~hatcher/3M/3Mdownloads.html).