Definition & Betydelse | Engelska ordet IMMERSIONS

Definition av IMMERSIONS

1. böjningsform av immersion

Exempel på hur man kan använda IMMERSIONS i en mening

• Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.
• The fact that it is homotopic is clear, since 3-space is contractible and thus all maps into it are homotopic, though the fact that this can be done through immersions requires some geometric argument.
• Roughly, the Whitney trick allows one to "unknot" knotted spheres – more precisely, remove self-intersections of immersions; it does this via a homotopy of a disk – the disk has 2 dimensions, and the homotopy adds 1 more – and thus in codimension greater than 2, this can be done without intersecting itself; hence embeddings in codimension greater than 2 can be understood by surgery.
• There are many applications of his results, including topological conditions for the existence of exact Lagrangian immersions and similar objects in symplectic and contact geometry.
• This baptistry was for many generations the only baptistery in Rome, and its domed octagonal structure, centered upon the large octagonal basin for full immersions, provided a model for others throughout Italy, and even an iconic motif of illuminated manuscripts, "The fountain of Life".
• In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such as immersions, submersions, covering spaces, and ramified covering spaces.
• Built on the same core offering of the Flexible Executive MBA, the Global Executive MBA is offered over 24 months for high-touch, fast-track learning and includes five international study visits and immersions in strategic global locations along with individualised executive coaching.
• Regular homotopy for immersions is similar to isotopy of embeddings: they are both restricted types of homotopies.
• Codimension 0 immersions are equivalently relative dimension 0 submersions, and are better thought of as submersions.
• Particularly topologically interesting classes of maps include embeddings, immersions, and submersions.
• In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such as immersions, submersions, covering spaces, and ramified covering spaces.
• This establishes that, under nonpositivity of the sectional curvature, abelian subgroups of the fundamental group are represented by geometrically special submanifolds: totally geodesic isometric immersions of a flat torus.
• In particular, he worked on rigidity and convexity of isometric immersions, stability of hypersurfaces and of minimal surfaces, topology of manifolds, isoperimetric problems, minimal submanifolds of a sphere, and manifolds of constant mean curvature and vanishing scalar curvature.
• Submanifolds of space forms which satisfy the equality case of this inequality are known as ideal immersions; such submanifolds are critical points of a certain restriction of the Willmore energy.
• 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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