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Manifold decomposition

Index Manifold decomposition

In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. [1]

32 relations: Adjunction space, Atoroidal, Closed manifold, Compact space, Connected sum, Critical point (mathematics), Differentiable manifold, Edwin E. Moise, Haken manifold, Handle decomposition, Handlebody, Heegaard splitting, Irreducibility (mathematics), JSJ decomposition, Link (knot theory), Manifold, Mathematics, Morse theory, Open book decomposition, Orientability, Poincaré conjecture, Prime decomposition (3-manifold), Prime manifold, Seifert fiber space, Simplex, Surface (topology), Surgery theory, Topology, Torus, Triangulation (topology), Trigenus, 3-manifold.

Adjunction space

In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another.

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Atoroidal

In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus.

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Closed manifold

In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.

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Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

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Critical point (mathematics)

In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.

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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

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Edwin E. Moise

Edwin Evariste Moise (December 22, 1918 – December 18, 1998) was an American mathematician and mathematics education reformer.

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Haken manifold

In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface.

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Handle decomposition

In mathematics, a handle decomposition of an m-manifold M is a union where each M_i is obtained from M_ by the attaching of i-handles.

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Handlebody

In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces.

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Heegaard splitting

In the mathematical field of geometric topology, a Heegaard splitting is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies.

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Irreducibility (mathematics)

In mathematics, the concept of irreducibility is used in several ways.

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JSJ decomposition

In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson.

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Link (knot theory)

In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Morse theory

"Morse function" redirects here.

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Open book decomposition

In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori.

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Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

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Poincaré conjecture

In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.

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Prime decomposition (3-manifold)

In mathematics, the prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite collection of prime 3-manifolds.

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Prime manifold

In topology (a mathematical discipline) a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds.

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Seifert fiber space

A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles.

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Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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Surgery theory

In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Triangulation (topology)

In mathematics, topology generalizes the notion of triangulation in a natural way as follows: Triangulation is useful in determining the properties of a topological space.

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Trigenus

In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple (g_1,g_2,g_3).

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3-manifold

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

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References

[1] https://en.wikipedia.org/wiki/Manifold_decomposition

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