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- Graph_manifold abstract "In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were invented and classified by the German topologist Friedhelm Waldhausen in 1967. This definition allows a very convenient combinatorial description as a graph whose vertices are the fundamental parts and (decorated) edges stand for the description of the gluing, hence the name.Two very important classes of examples are given by the Seifert bundles and the Solv manifolds. This leads to a more modern definition: a graph manifold is either a Solv manifold, a manifold having only Seifert pieces in its JSJ decomposition, or connect sums of the previous two categories. From this perspective, Waldhausen's article can be seen as the first breakthrough towards the discovery of JSJ decomposition. One of the numerous consequences of the Thurston-Perelman geometrization theorem is that graph manifolds are precisely the 3-manifolds whose Gromov norm vanishes.".
- Graph_manifold wikiPageID "1857439".
- Graph_manifold wikiPageLength "1778".
- Graph_manifold wikiPageOutDegree "12".
- Graph_manifold wikiPageRevisionID "610459824".
- Graph_manifold wikiPageWikiLink 3-manifold.
- Graph_manifold wikiPageWikiLink Category:3-manifolds.
- Graph_manifold wikiPageWikiLink Circle_bundle.
- Graph_manifold wikiPageWikiLink Friedhelm_Waldhausen.
- Graph_manifold wikiPageWikiLink Geometrization_conjecture.
- Graph_manifold wikiPageWikiLink Gromov_norm.
- Graph_manifold wikiPageWikiLink Inventiones_Mathematicae.
- Graph_manifold wikiPageWikiLink JSJ_decomposition.
- Graph_manifold wikiPageWikiLink Seifert_fiber_space.
- Graph_manifold wikiPageWikiLink Seifert_fiber_spaces.
- Graph_manifold wikiPageWikiLink Thurston_geometry.
- Graph_manifold wikiPageWikiLink Topology.
- Graph_manifold wikiPageWikiLinkText "Graph manifold".
- Graph_manifold wikiPageWikiLinkText "graph manifold".
- Graph_manifold hasPhotoCollection Graph_manifold.
- Graph_manifold wikiPageUsesTemplate Template:Citation.
- Graph_manifold wikiPageUsesTemplate Template:Topology-stub.
- Graph_manifold subject Category:3-manifolds.
- Graph_manifold hypernym Manifold.
- Graph_manifold comment "In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were invented and classified by the German topologist Friedhelm Waldhausen in 1967.".
- Graph_manifold label "Graph manifold".
- Graph_manifold sameAs m.061h_x.
- Graph_manifold sameAs Граф-многовид.
- Graph_manifold sameAs Q4148033.
- Graph_manifold sameAs Q4148033.
- Graph_manifold wasDerivedFrom Graph_manifold?oldid=610459824.
- Graph_manifold isPrimaryTopicOf Graph_manifold.