branch of mathematics, a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that...

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...

a 3-manifold M {\displaystyle M} which cannot be described as a connected sum of two 3-manifolds is called prime. For the case of a 3-manifold given...

beverages Prime Books, an American publisher Prime (finance) Prime rate, a rate of interest applied in banking Prime (order theory) Prime 3-manifold, a 3-manifold...

connected sum of prime knots. The prime decomposition of 3-manifolds is another example of this type. Beyond mathematics and computing, prime numbers have...

In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must...

{\displaystyle S^{3}} . All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds. A special case of the...

called prime, if it cannot be written as a connected sum of two n-manifolds (neither of which is an n-sphere). An irreducible manifold is thus prime, although...

geometrization conjecture. A 3-manifold is called closed if it is compact and has no boundary. Every closed 3-manifold has a prime decomposition: this means...

mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a...

topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n-space, in which the number n is the manifold's dimension...

manifolds. A manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has...

finite time extinction. It is equivalent to saying that the prime decomposition of the manifold has no acyclic components and turns out to be equivalent...

John Streeter Manifold AM (21 April 1915 – 19 April 1985) was an Australian poet and critic. He was born in Melbourne, into a well known Camperdown family...

In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} ...

charge from each turbocharger into a single intake manifold, while others use a separate intake manifold for each turbocharger. Parallel configurations are...

is a double-cover of the Gieseking manifold, which has the smallest volume among non-compact hyperbolic 3-manifolds. The figure-eight knot and the (−2...

geometrization conjecture Hyperbolic 3-manifolds Spherical 3-manifolds Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert...

smooth manifold, R is the ring of smooth real functions on M, and x is a point in M, then the set of all smooth functions f with f (x) = 0 forms a prime ideal...

of multivariable calculus topics Manifold Differentiable manifold Smooth manifold Banach manifold Fréchet manifold Tensor analysis Tangent vector Tangent...

every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold 1613, 1607 and 1619 are all primes 1614 = number of ways of refining the...

the Fubini–Study metric, such a manifold is always a Kähler manifold. By Chow's theorem, a projective complex manifold is also a smooth projective algebraic...

known as Cartan–Hadamard manifolds? Chern's conjecture (affine geometry) that the Euler characteristic of a compact affine manifold vanishes. Chern's conjecture...

of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction...

concerns functions between differentiable or smooth manifolds. Intuitively speaking such a manifold M {\displaystyle M} is a space that can be approximated...

M as a Riemannian manifold can be recovered from this data. This suggests that one might define a noncommutative Riemannian manifold as a spectral triple...

groups of manifolds; and in particular with the limitations on topological groups G that can act effectively (faithfully) on a (topological) manifold M. Restricting...

f ′ ( x ) , f ′ ′ ( x ) , … , f ( k ) ( x ) {\textstyle f^{\prime }(x),f^{\prime \prime }(x),\ldots ,f^{(k)}(x)} exist and are continuous over the domain...

adding more structure, one may view the plane as a 1-dimensional complex manifold, called the complex line. Many fundamental tasks in mathematics, geometry...

is a diffeomorphism of a differentiable manifold, so that the derivative f n ′ {\displaystyle f_{n}^{\prime }} is defined, then one says that a periodic...