3-manifolds

JSJ decomposition

In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: Irreducible orientable closed (i.e., compact and without boundary) 3-manifolds have a unique (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. The acronym JSJ is for William Jaco, Peter Shalen, and . The first two worked together, and the third worked independently. (Wikipedia).

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Set Up the Partial Fraction Decomposition. Just setting them up. See my other videos for actual solved problems.

From playlist Partial Fraction Decomposition

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Find the Partial Fraction Decomposition 3x/((x + 1)(x^2 + 1))

From playlist Partial Fraction Decomposition

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From playlist Matrix Equations

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From playlist Matrix Equations

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From playlist Graph Theory

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From playlist Orthogonality

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The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups. Later, the JSJ was genera

From playlist Geometry in non-positive curvature and Kähler groups

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Find the Partial Fraction Decomposition 2x/((x - 1)(x + 2)

From playlist Partial Fraction Decomposition

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Partial Fraction Decomposition Repeated Linear Factors 2x/((x + 1)(x + 2)^2)

From playlist Partial Fraction Decomposition

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From playlist Mathematics

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Gilbert Levitt - Vertex finiteness for relatively hyperbolic groups

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From playlist A second course in university calculus.

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From playlist Virtual Conference

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From playlist Mathematics

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LU decomposition of matrices

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From playlist Introducing linear algebra

Related pages

Incompressible surface | Atoroidal | Geometrization conjecture | Mathematics | Homotopy | Manifold decomposition | 3-manifold | Embedding | Mapping torus | Torus | Orientability | Satellite knot