Homotopy groups of spheres — In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure… … Wikipedia
Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… … Wikipedia
Sphère exotique — En mathématiques, et plus précisément en topologie différentielle, une sphère exotique est une variété différentielle M qui est homéomorphe, mais non difféomorphe, à la n sphère euclidienne standard. Autrement dit, M est une sphère du point de… … Wikipédia en Français
Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… … Wikipedia
N-sphere — can project a sphere s surface to a plane, it can also project a 3 sphere s surface into 3 space. This image shows three coordinate directions projected to 3 space:parallels (red), meridians (blue) and hypermeridians (green).Due to the conformal… … Wikipedia
n-sphere — 2 sphere wireframe as an orthogonal projection Just as a … Wikipedia
Exotic sphere — In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n sphere. That is, M is a sphere from the point of view of all its… … Wikipedia
Contractibility of unit sphere in Hilbert space — In topology, it is a surprising fact that the unit sphere in (infinite dimensional) Hilbert space is a contractible space, sinceno finite dimensional spheres are contractible.This can be demonstrated in several different ways. Topological proof… … Wikipedia
Regular homotopy — In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. In particular, the homotopy must go through immersions and extend continuously to a homotopy of the… … Wikipedia
3-sphere — Stereographic projection of the hypersphere s parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles … Wikipedia
