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- Prime_manifold abstract "In topology (a mathematical discipline) a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither of the two is an n-sphere.A similar notion is that of an irreducible n-manifold, which is one in which any embedded (n − 1)-sphere bounds an embedded n-ball. Implicit in this definition is the use of a suitable category, such as the category of differentiable manifolds or the category of piecewise-linear manifolds.The notions of irreducibility in algebra and manifold theory are related. An irreducible manifold is prime, although the converse does not hold. From an algebraist's perspective, prime manifolds should be called "irreducible"; however the topologist (in particular the 3-manifold topologist) finds the definition above more useful. The only compact, connected 3-manifolds that are prime but not irreducible are the trivial 2-sphere bundle over the circle S1 and the twisted 2-sphere bundle over S1.According to a theorem of Hellmuth Kneser and John Milnor, every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) collection of prime 3-manifolds.".
- Prime_manifold wikiPageID "19045780".
- Prime_manifold wikiPageLength "6646".
- Prime_manifold wikiPageOutDegree "42".
- Prime_manifold wikiPageRevisionID "626381233".
- Prime_manifold wikiPageWikiLink 3-manifold.
- Prime_manifold wikiPageWikiLink 3-sphere.
- Prime_manifold wikiPageWikiLink Alexander_horned_sphere.
- Prime_manifold wikiPageWikiLink Alexanders_horned_sphere.
- Prime_manifold wikiPageWikiLink Ball_(mathematics).
- Prime_manifold wikiPageWikiLink Ball_(topology).
- Prime_manifold wikiPageWikiLink Category:Manifolds.
- Prime_manifold wikiPageWikiLink Category_theory.
- Prime_manifold wikiPageWikiLink Compact_space.
- Prime_manifold wikiPageWikiLink Connected_space.
- Prime_manifold wikiPageWikiLink Connected_sum.
- Prime_manifold wikiPageWikiLink Curve.
- Prime_manifold wikiPageWikiLink Differentiable_manifold.
- Prime_manifold wikiPageWikiLink Euclidean_space.
- Prime_manifold wikiPageWikiLink Fiber_bundle.
- Prime_manifold wikiPageWikiLink Hellmuth_Kneser.
- Prime_manifold wikiPageWikiLink Homeomorphic.
- Prime_manifold wikiPageWikiLink Homeomorphism.
- Prime_manifold wikiPageWikiLink John_Milnor.
- Prime_manifold wikiPageWikiLink Lens_space.
- Prime_manifold wikiPageWikiLink Manifold.
- Prime_manifold wikiPageWikiLink Manifold_(topology).
- Prime_manifold wikiPageWikiLink N-sphere.
- Prime_manifold wikiPageWikiLink Non-orientable.
- Prime_manifold wikiPageWikiLink Orientability.
- Prime_manifold wikiPageWikiLink Piecewise-linear_manifold.
- Prime_manifold wikiPageWikiLink Piecewise_linear_manifold.
- Prime_manifold wikiPageWikiLink Prime_decomposition_(3-manifold).
- Prime_manifold wikiPageWikiLink Product_space.
- Prime_manifold wikiPageWikiLink Product_topology.
- Prime_manifold wikiPageWikiLink Submanifold.
- Prime_manifold wikiPageWikiLink Topology.
- Prime_manifold wikiPageWikiLink Tubular_neighborhood.
- Prime_manifold wikiPageWikiLink Up_to.
- Prime_manifold wikiPageWikiLink William_Jaco.
- Prime_manifold wikiPageWikiLinkText "Prime manifold".
- Prime_manifold wikiPageWikiLinkText "prime 3-manifold".
- Prime_manifold hasPhotoCollection Prime_manifold.
- Prime_manifold wikiPageUsesTemplate Template:Cite_book.
- Prime_manifold subject Category:Manifolds.
- Prime_manifold type Space.
- Prime_manifold comment "In topology (a mathematical discipline) a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither of the two is an n-sphere.A similar notion is that of an irreducible n-manifold, which is one in which any embedded (n − 1)-sphere bounds an embedded n-ball.".
- Prime_manifold label "Prime manifold".
- Prime_manifold sameAs 3-varietà_irriducibile.
- Prime_manifold sameAs m.0j4469m.
- Prime_manifold sameAs Q3598797.
- Prime_manifold sameAs Q3598797.
- Prime_manifold wasDerivedFrom Prime_manifold?oldid=626381233.
- Prime_manifold isPrimaryTopicOf Prime_manifold.