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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 wikiPageRevisionID "579769490".
- Prime_manifold hasPhotoCollection Prime_manifold.
- Prime_manifold subject Category:Manifolds.
- Prime_manifold type Artifact100021939.
- Prime_manifold type Conduit103089014.
- Prime_manifold type Manifold103717750.
- Prime_manifold type Manifolds.
- Prime_manifold type Object100002684.
- Prime_manifold type Passage103895293.
- Prime_manifold type PhysicalEntity100001930.
- Prime_manifold type Pipe103944672.
- Prime_manifold type Tube104493505.
- Prime_manifold type Way104564698.
- Prime_manifold type Whole100003553.
- Prime_manifold type YagoGeoEntity.
- Prime_manifold type YagoPermanentlyLocatedEntity.
- 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 "3-varietà irriducibile".
- 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 sameAs Prime_manifold.
- Prime_manifold wasDerivedFrom Prime_manifold?oldid=579769490.
- Prime_manifold isPrimaryTopicOf Prime_manifold.