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.
New!!: Manifold decomposition and Adjunction space · See more »
Atoroidal
In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus.
New!!: Manifold decomposition and Atoroidal · See more »
Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
New!!: Manifold decomposition and Closed manifold · See more »
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).
New!!: Manifold decomposition and Compact space · See more »
Connected sum
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.
New!!: Manifold decomposition and Connected sum · See more »
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.
New!!: Manifold decomposition and Critical point (mathematics) · See more »
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.
New!!: Manifold decomposition and Differentiable manifold · See more »
Edwin E. Moise
Edwin Evariste Moise (December 22, 1918 – December 18, 1998) was an American mathematician and mathematics education reformer.
New!!: Manifold decomposition and Edwin E. Moise · See more »
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.
New!!: Manifold decomposition and Haken manifold · See more »
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.
New!!: Manifold decomposition and Handle decomposition · See more »
Handlebody
In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces.
New!!: Manifold decomposition and Handlebody · See more »
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.
New!!: Manifold decomposition and Heegaard splitting · See more »
Irreducibility (mathematics)
In mathematics, the concept of irreducibility is used in several ways.
New!!: Manifold decomposition and Irreducibility (mathematics) · See more »
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.
New!!: Manifold decomposition and JSJ decomposition · See more »
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.
New!!: Manifold decomposition and Link (knot theory) · See more »
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
New!!: Manifold decomposition and Manifold · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Manifold decomposition and Mathematics · See more »
Morse theory
"Morse function" redirects here.
New!!: Manifold decomposition and Morse theory · See more »
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.
New!!: Manifold decomposition and Open book decomposition · See more »
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.
New!!: Manifold decomposition and Orientability · See more »
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.
New!!: Manifold decomposition and Poincaré conjecture · See more »
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.
New!!: Manifold decomposition and Prime decomposition (3-manifold) · See more »
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.
New!!: Manifold decomposition and Prime manifold · See more »
Seifert fiber space
A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles.
New!!: Manifold decomposition and Seifert fiber space · See more »
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
New!!: Manifold decomposition and Simplex · See more »
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.
New!!: Manifold decomposition and Surface (topology) · See more »
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.
New!!: Manifold decomposition and Surgery theory · See more »
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.
New!!: Manifold decomposition and Topology · See more »
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.
New!!: Manifold decomposition and Torus · See more »
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.
New!!: Manifold decomposition and Triangulation (topology) · See more »
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).
New!!: Manifold decomposition and Trigenus · See more »
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.
New!!: Manifold decomposition and 3-manifold · See more »
References
[1] https://en.wikipedia.org/wiki/Manifold_decomposition