Fibered manifold information

differentiable fiber bundle is a fibered manifold. Every differentiable covering space is a fibered manifold with discrete fiber. In general, a fibered manifold need...

bundle. The theory of fibered spaces, of which vector bundles, principal bundles, topological fibrations and fibered manifolds are a special case, is...

each fiber has a tubular neighborhood that forms a standard fibered torus. A standard fibered torus corresponding to a pair of coprime integers ( a , b...

(N, h) be two Riemannian manifolds and f : M → N {\displaystyle f:M\to N} a (surjective) submersion, i.e., a fibered manifold. The horizontal distribution...

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...

manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...

ISBN 9783110808056. Otal, Jean-Pierre (2001), The hyperbolization theorem for fibered 3-manifolds, Contemporary Mathematics, vol. 7, American Mathematical Society...

Geometrization conjecture Manifold decomposition Satellite knot Jaco, William H.; Shalen, Peter B (1979), "Seifert fibered spaces in 3-manifolds", Memoirs of the...

F_{i}} of motion. Their level surfaces (invariant submanifolds) form a fibered manifold F : Z → N = F ( Z ) {\displaystyle F:Z\to N=F(Z)} over a connected...

as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise"...

In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every...

In mathematics, a differentiable manifold M {\displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields { V 1 , … , V...

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...

geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely, a Hermitian manifold is a complex manifold with a smoothly...

for example sphere bundles are fibered by spheres. A vector bundle (E, p, M) is smooth, if E and M are smooth manifolds, p: E → M is a smooth map, and...

fibration: the problem is that some fibers may "reverse orientation"; in other words their neighborhoods look like fibered solid Klein bottles rather than...

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

} called the linear derivative of Φ {\displaystyle \Phi } . Fiber bundle Fibered manifold Vector bundle Affine space Kolář, Ivan; Michor, Peter; Slovák...

knot, and figure-eight knot are fibered knots. The Hopf link is a fibered link. The Alexander polynomial of a fibered knot is monic, i.e. the coefficients...

automorphisms of so-called natural fiber bundles. Let π : Y → X {\displaystyle \pi :Y\to X} be a fibered manifold with local fibered coordinates ( x λ , y i )...

} The complement of a torus knot in the 3-sphere is a Seifert-fibered manifold, fibred over the disc with two singular fibres. Let Y be the p-fold...