homology sphere

homology sphere
A manifold whose homology is the same as that of some sphere of the same dimension

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  • Homology 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 …   Wikipedia

  • Homology manifold — In mathematics, a homology manifold (or generalized manifold)is a locally compact topological space X that looks locally like a topological manifold from the point of view of homology theory.DefinitionA homology G manifold (without boundary) of… …   Wikipedia

  • homology — /heuh mol euh jee, hoh /, n., pl. homologies. 1. the state of being homologous; homologous relation or correspondence. 2. Biol. a. a fundamental similarity based on common descent. b. a structural similarity of two segments of one animal based on …   Universalium

  • 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

  • Homotopy sphere — In algebraic topology, a branch of mathematics, a homotopy sphere is an n manifold homotopy equivalent to the n sphere. It thus has the same homotopy groups and the same homology groups, as the n sphere. So every homotopy sphere is an homology… …   Wikipedia

  • n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

  • 3-sphère — Projection stéréographique des parallèles (en rouge) des méridiens (en bleu) et des hyperméridiens (en vert) de l hypersphère : ce sont les lignes sur lesquelles une seule des coordonnées hypersphériques varie (voir le texte). À cause des… …   Wikipédia en Français

  • Poincaré sphere — Poincaré sphere, often spelled Poincare sphere (ie without the accent) may refer to: * Poincaré sphere, in polarimetry, a visualization of polarized light * Poincaré homology sphere, in mathematics, an example of a homology sphere …   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

  • Casson invariant — In 3 dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer valued invariant of oriented integral homology 3 spheres, introduced by Andrew Casson.Kevin Walker (1992) found an extension to… …   Wikipedia

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