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- Lens_space abstract "A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions.In the 3-manifold case, a lens space can be visualized as the result of gluing two solid tori together by a homeomorphism of their boundaries. Often the 3-sphere and , both of which can be obtained as above, are not counted as they are considered trivial special cases.The three-dimensional lens spaces were introduced by Tietze in 1908. They were the first known examples of 3-manifolds which were not determined by their homology and fundamental group alone, and the simplest examples of closed manifolds whose homeomorphism type is not determined by their homotopy type. J.W. Alexander in 1919 showed that the lens spaces and were not homeomorphic even though they have isomorphic fundamental groups and the same homology, though they do not have the same homotopy type. Other lens spaces have even the same homotopy type (and thus isomorphic fundamental groups and homology), but not the same homeomorphism type; they can thus be seen as the birth of geometric topology of manifolds as distinct from algebraic topology. There is a complete classification of three-dimensional lens spaces, by fundamental group and Reidemeister torsion.".
- Lens_space wikiPageExternalLink Fake_lens_spaces.
- Lens_space wikiPageExternalLink Lens_spaces.
- Lens_space wikiPageExternalLink Lens_spaces:_a_history.
- Lens_space wikiPageExternalLink 3Mdownloads.html.
- Lens_space wikiPageExternalLink ATpage.html.
- Lens_space wikiPageExternalLink Tietze1908.pdf.
- Lens_space wikiPageExternalLink tietze.pdf.
- Lens_space wikiPageExternalLink lensspaces.pdf.
- Lens_space wikiPageID "885725".
- Lens_space wikiPageRevisionID "565788605".
- Lens_space hasPhotoCollection Lens_space.
- Lens_space subject Category:3-manifolds.
- Lens_space subject Category:Manifolds.
- Lens_space type Artifact100021939.
- Lens_space type Conduit103089014.
- Lens_space type Manifold103717750.
- Lens_space type Manifolds.
- Lens_space type Object100002684.
- Lens_space type Passage103895293.
- Lens_space type PhysicalEntity100001930.
- Lens_space type Pipe103944672.
- Lens_space type Tube104493505.
- Lens_space type Way104564698.
- Lens_space type Whole100003553.
- Lens_space type YagoGeoEntity.
- Lens_space type YagoPermanentlyLocatedEntity.
- Lens_space comment "A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions.In the 3-manifold case, a lens space can be visualized as the result of gluing two solid tori together by a homeomorphism of their boundaries.".
- Lens_space label "Espace lenticulaire".
- Lens_space label "Lens space".
- Lens_space label "Lensruimten van Tietze".
- Lens_space label "Spazio lenticolare".
- Lens_space label "Линзовое пространство".
- Lens_space label "レンズ空間".
- Lens_space sameAs Espace_lenticulaire.
- Lens_space sameAs Spazio_lenticolare.
- Lens_space sameAs レンズ空間.
- Lens_space sameAs 렌즈_공간.
- Lens_space sameAs Lensruimten_van_Tietze.
- Lens_space sameAs m.03lrc8.
- Lens_space sameAs Q2470499.
- Lens_space sameAs Q2470499.
- Lens_space sameAs Lens_space.
- Lens_space wasDerivedFrom Lens_space?oldid=565788605.
- Lens_space isPrimaryTopicOf Lens_space.