gluing sphere
13-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 …
2Exotic 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… …
3n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …
4N-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… …
5Homology sphere — In algebraic topology, a homology sphere is an n manifold X having the homology groups of an n sphere, for some integer n ≥ 1. That is, we have: H 0( X ,Z) = Z = H n ( X ,Z)and : H i ( X ,Z) = {0} for all other i .Therefore X is a connected space …
6Alexander horned sphere — The Alexander horned sphere is one of the most famous pathological examples in mathematics discovered in 1924 by J. W. Alexander. It is the particular embedding of a sphere in 3 dimensional Euclidean space obtained by the following construction,… …
7Handle decomposition — In mathematics, a handle decomposition of an n manifold M is a representation of that manifold as an exhaustion:M 0 subset M 1 subset dots subset Mwhere each M i is obtained from M {i 1}by attaching a n i handle. Handle decompositions are never… …
8Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …
9Orbifold — This terminology should not be blamed on me. It was obtained by a democratic process in my course of 1976 77. An orbifold is something with many folds; unfortunately, the word “manifold” already has a different definition. I tried “foldamani”,… …
10Connected sum — In mathematics, specifically in topology, the operation 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 plays a key role in the… …
