Homology Sphere

(Homology Theory)

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Homology Theory
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What is Homology sphere?

In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer . That is, and for all other i. Therefore X is a connected space, with one non-zero higher Betti number, namely, . It does not follow that X is simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but using homology with rational coefficients.

Technology Types

homology theorymathematical spacesetspacespheretopological space

Synonyms

Homology 3-spherePoincare 3-spherePoincare dodecahedral spacePoincaré dodecahedral spacePoincare homology spherePoincaré homology sphereRational homology 3-sphere

Translations

Esfera homológica (es)Homologiesphäre (de)Sphère d'homologie (fr)Гомологическая сфера (ru)Сфера Пуанкаре (uk)同調球面 (zh)

Tech Info


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