Anagram & Information om | Engelska ordet FIBRATION

Exempel på hur man kan använda FIBRATION i en mening

• With the pathspace construction, any continuous mapping can be extended to a fibration by enlarging its domain to a homotopy equivalent space.
• They also provide a canonical example of Hopf fibration, where the geodesic flow induced by the linear fractional transformation decomposes complex projective space into stable and unstable manifolds, with the horocycles appearing perpendicular to the geodesics.
• In differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.
• For example, for the minimal genus 1 fibration of a (quasi)-bielliptic surface induced by the Albanese morphism, the canonical bundle formula gives that this fibration has no multiple fibers.
• In these cases, the family of Seifert surfaces is an aspect of the Milnor fibration of the singularity.
• The Hopf link is named after topologist Heinz Hopf, who considered it in 1931 as part of his research on the Hopf fibration.
• However, it is sometimes possible for two Seifert manifolds to be homeomorphic even if they have different normalized symbols, because a few manifolds (such as lens spaces) can have more than one sort of Seifert fibration.
• The most studied Milnor maps are actually fibrations, and the phrase Milnor fibration is more commonly encountered in the mathematical literature.
• A fibration that is also a weak equivalence is called an acyclic (or trivial) fibration and a cofibration that is also a weak equivalence is called an acyclic (or trivial) cofibration (or sometimes called an anodyne morphism).
• Frédéric Campana conjectured that a variety is potentially dense if and only if it has no rational fibration over a positive-dimensional orbifold of general type.
• The two pentagonal antiprism tubes, plus the 10 BC helices, form an irregular discrete Hopf fibration of the grand antiprism that Hopf maps to the faces of a pentagonal antiprism.
• A stack is a groupoid fibration satisfied further glueing properties, expressed in terms of descent.
• In particular, category fibered in groupoids over another category is a special case of a right fibration of simplicial sets in the ∞-category setup.
• The mathematical topics visualized in these chapters include the Penrose triangle and related optical illusions; the Roman surface and Boy's surface, two different immersions of the projective plane, and deformations between them; sphere eversion and the Morin surface; group theory, the mapping class groups of surfaces, and the braid groups; and knot theory, Seifert surfaces, the Hopf fibration of space by linked circles, and the construction of knot complements by gluing polyhedra.

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