JSJ decomposition

The Jaco - Shalen - Johannson decomposition, abbreviated JSJ decomposition, named after William Jaco, Shalen Peter and Klaus Johannson, is a statement from the topology of 3-manifolds.

Statement

It says that every irreducible 3 -dimensional manifold has a unique (up to isotopy ) Seifert fibered submanifold with atoroidalem complement.

Evidence

The proof was carried out in 1979 by William Jaco and Peter Shalen and, independently of these, by Klaus Johannson.

Consequences

The JSJ decomposition is an important prerequisite for the geometrization of 3- manifolds. Each Seifert - fibred manifold can be geometricize, and proven by Grigori Perelman Thurston 's conjecture states that every atoroidale irreducible 3-manifold carries a hyperbolic metric.

Swell

  • Geometric topology
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