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- Mapping_torus abstract "In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the static homeomorphism:The result is a fiber bundle whose base is a circle and whose fiber is the original space X. If X is a manifold, Mf will be a manifold of dimension one higher, and it is said to "fiber over the circle". Mapping tori of surface homeomorphisms play a key role in the theory of 3-manifolds and have been intensely studied. If S is a closed surface of genus g ≥ 2 and if f is a self-homeomorphism of S, the mapping torus Mf is a closed 3-manifold that fibers over the circle with fiber S. A deep result of Thurston states that in this case the 3-manifold Mf is hyperbolic if and only if f is a pseudo-Anosov homeomorphism of S.".
- Mapping_torus wikiPageID "21034384".
- Mapping_torus wikiPageRevisionID "545539710".
- Mapping_torus hasPhotoCollection Mapping_torus.
- Mapping_torus subject Category:General_topology.
- Mapping_torus subject Category:Geometric_topology.
- Mapping_torus subject Category:Homeomorphisms.
- Mapping_torus comment "In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the static homeomorphism:The result is a fiber bundle whose base is a circle and whose fiber is the original space X. If X is a manifold, Mf will be a manifold of dimension one higher, and it is said to "fiber over the circle".".
- Mapping_torus label "Abbildungstorus".
- Mapping_torus label "Mapping torus".
- Mapping_torus label "Tore d'application".
- Mapping_torus sameAs Abbildungstorus.
- Mapping_torus sameAs Tore_d'application.
- Mapping_torus sameAs m.08k96p.
- Mapping_torus sameAs Q3532262.
- Mapping_torus sameAs Q3532262.
- Mapping_torus wasDerivedFrom Mapping_torus?oldid=545539710.
- Mapping_torus isPrimaryTopicOf Mapping_torus.