Ending lamination theorem (original) (raw)
In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold. and proved the ending lamination conjecture for Kleinian surface groups. In view of the Tameness theorem this implies the ending lamination conjecture for all finitely generated Kleinian groups, from which the general case of ELT follows.
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| dbo:abstract | In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold. The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume. When the manifold is compact or of finite volume, the Mostow rigidity theorem states that the fundamental group determines the manifold. When the volume is infinite the fundamental group is not enough to determine the manifold: one also needs to know the hyperbolic structure on the surfaces at the "ends" of the manifold, and also the ending laminations on these surfaces. and proved the ending lamination conjecture for Kleinian surface groups. In view of the Tameness theorem this implies the ending lamination conjecture for all finitely generated Kleinian groups, from which the general case of ELT follows. (en) |
| dbo:wikiPageExternalLink | http://math.yale.edu/~yhm3/research/ https://books.google.com/books%3Fid=w0IYCTiXOm4C http://library.msri.org/books/gt3m/ http://annals.math.princeton.edu/2012/176-1 |
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| dbo:wikiPageWikiLink | dbr:Cambridge_University_Press dbr:Mostow_rigidity_theorem dbr:Annals_of_Mathematics dbc:3-manifolds dbc:Kleinian_groups dbr:Fundamental_group dbr:Lamination_(topology) dbc:Hyperbolic_geometry dbr:Hyperbolic_3-manifold dbr:Hyperbolic_geometry dbr:Kleinian_group dbr:Tameness_theorem dbr:Finitely-generated_group dbr:Surface_group |
| dbp:authorlink | William Thurston (en) |
| dbp:first | William (en) |
| dbp:last | Thurston (en) |
| dbp:wikiPageUsesTemplate | dbt:Citation dbt:Harvtxt dbt:Harvs |
| dbp:year | 1982 (xsd:integer) |
| dcterms:subject | dbc:3-manifolds dbc:Kleinian_groups dbc:Hyperbolic_geometry |
| gold:hypernym | dbr:Laminations |
| rdf:type | yago:Abstraction100002137 yago:Group100031264 yago:WikicatKleinianGroups |
| rdfs:comment | In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold. and proved the ending lamination conjecture for Kleinian surface groups. In view of the Tameness theorem this implies the ending lamination conjecture for all finitely generated Kleinian groups, from which the general case of ELT follows. (en) |
| rdfs:label | Ending lamination theorem (en) |
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