About: Prime manifold

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Prime manifold Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Whole100003553, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/6at915WXBT

In topology, a branch of mathematics, 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.

Attributes	Values
rdf:type	yago:WikicatManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	3-varietà irriducibile (it) Prime manifold (en)
rdfs:comment	In topology, a branch of mathematics, 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. (en) In geometria, e più precisamente nella topologia della dimensione bassa, una 3-varietà irriducibile è una 3-varietà in cui ogni sfera borda una palla. Una 3-varietà che contiene una sfera non bordante una palla è invece detta riducibile: questa può essere effettivamente "ridotta" a una varietà più semplice tramite l'operazione inversa della somma connessa. (it)
dct:subject	Manifolds
Wikipage page ID	19045780 (xsd:integer)
Wikipage revision ID	1054280673 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime decomposition (3-manifold) Product topology Homeomorphic Curve Compact space Mathematics Boundary (topology) N-sphere Connected space Connected sum Submanifold Topology 3-sphere 3-manifold Manifolds Euclidean space Fiber bundle Lens space Hellmuth Kneser Abstract algebra John Milnor Homeomorphism Tubular neighborhood Differentiable manifold Orientability Category (mathematics) Up to Non-orientable Manifold (topology) Piecewise-linear manifold Alexander's horned sphere Ball (topology)
sameAs	Prime manifold Prime manifold Prime manifold Prime manifold Prime manifold
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Visible_anchor dbt:Manifolds
has abstract	In topology, a branch of mathematics, 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. (en) In geometria, e più precisamente nella topologia della dimensione bassa, una 3-varietà irriducibile è una 3-varietà in cui ogni sfera borda una palla. Una 3-varietà che contiene una sfera non bordante una palla è invece detta riducibile: questa può essere effettivamente "ridotta" a una varietà più semplice tramite l'operazione inversa della somma connessa. Una 3-varietà è prima se non è ottenuta come somma connessa non banale di due varietà. I concetti di irriducibile e prima sono equivalenti per tutte le 3-varietà, con due sole eccezioni. L'ipotesi di irriducibilità è però più facile da esprimere e da gestire in molti casi, ed è quindi quella usata più spesso. (it)
prov:wasDerivedFrom	wikipedia-en:Prime_manifold?oldid=1054280673&ns=0
page length (characters) of wiki page	6856 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Prime_manifold
is Link from a Wikipage to another Wikipage of	Prime decomposition of 3-manifolds Incompressible surface Geometrization conjecture 3-manifold Manifold decomposition Spherical 3-manifold Irreducible manifold
is Wikipage redirect of	Irreducible manifold
is foaf:primaryTopic of	wikipedia-en:Prime_manifold

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3331 as of Sep 2 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 52 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software