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- Surface_bundle_over_the_circle abstract "In mathematics, a surface bundle over the circle is a fiber bundle with base space a circle, and with fiber space a surface. Therefore the total space has dimension 2 + 1 = 3. In general, fiber bundles over the circle are a special case of mapping tori.Here is the construction: take the Cartesian product of a surface with the unit interval. Glue the two copies of the surface, on the boundary, by some homeomorphism. This homeomorphism is called the monodromy of the surface bundle. It is possible to show that the homeomorphism type of the bundle obtained depends only on the conjugacy class, in the mapping class group, of the gluing homeomorphism chosen. This construction is an important source of examples both in the field of low-dimensional topology as well as in geometric group theory. In the former we find that the geometry of the three-manifold is determined by the dynamics of the homeomorphism. This is the fibered part of Thurston's geometrization theorem for Haken manifolds, whose proof requires the Nielsen–Thurston classification for surface homeomorphisms as well as deep results in the theory of Kleinian groups. In geometric group theory the fundamental groups of such bundles give an important class of HNN-extensions: that is, extensions of the fundamental group of the fiber (a surface) by the integers.A simple special case of this construction (considered in Poincaré's foundational paper) is that of a torus bundle.".
- Surface_bundle_over_the_circle wikiPageID "2011690".
- Surface_bundle_over_the_circle wikiPageLength "1793".
- Surface_bundle_over_the_circle wikiPageOutDegree "27".
- Surface_bundle_over_the_circle wikiPageRevisionID "342664314".
- Surface_bundle_over_the_circle wikiPageWikiLink Cartesian_product.
- Surface_bundle_over_the_circle wikiPageWikiLink Category:3-manifolds.
- Surface_bundle_over_the_circle wikiPageWikiLink Category:Fiber_bundles.
- Surface_bundle_over_the_circle wikiPageWikiLink Circle.
- Surface_bundle_over_the_circle wikiPageWikiLink Conjugacy_class.
- Surface_bundle_over_the_circle wikiPageWikiLink Fiber_bundle.
- Surface_bundle_over_the_circle wikiPageWikiLink Fundamental_group.
- Surface_bundle_over_the_circle wikiPageWikiLink Geometric_group_theory.
- Surface_bundle_over_the_circle wikiPageWikiLink Geometry.
- Surface_bundle_over_the_circle wikiPageWikiLink Group_extension.
- Surface_bundle_over_the_circle wikiPageWikiLink HNN_extension.
- Surface_bundle_over_the_circle wikiPageWikiLink Henri_Poincaré.
- Surface_bundle_over_the_circle wikiPageWikiLink Integer.
- Surface_bundle_over_the_circle wikiPageWikiLink Kleinian_group.
- Surface_bundle_over_the_circle wikiPageWikiLink Low-dimensional_topology.
- Surface_bundle_over_the_circle wikiPageWikiLink Mapping_class_group.
- Surface_bundle_over_the_circle wikiPageWikiLink Mapping_torus.
- Surface_bundle_over_the_circle wikiPageWikiLink Mathematics.
- Surface_bundle_over_the_circle wikiPageWikiLink Monodromy.
- Surface_bundle_over_the_circle wikiPageWikiLink Nielsen–Thurston_classification.
- Surface_bundle_over_the_circle wikiPageWikiLink Surface.
- Surface_bundle_over_the_circle wikiPageWikiLink Torus_bundle.
- Surface_bundle_over_the_circle wikiPageWikiLink Unit_interval.
- Surface_bundle_over_the_circle wikiPageWikiLink Virtually_fibered_conjecture.
- Surface_bundle_over_the_circle wikiPageWikiLinkText "Surface bundle over the circle".
- Surface_bundle_over_the_circle wikiPageWikiLinkText "surface bundle over the circle".
- Surface_bundle_over_the_circle wikiPageWikiLinkText "surface bundles over the circle".
- Surface_bundle_over_the_circle wikiPageUsesTemplate Template:Unreferenced.
- Surface_bundle_over_the_circle subject Category:3-manifolds.
- Surface_bundle_over_the_circle subject Category:Fiber_bundles.
- Surface_bundle_over_the_circle hypernym Bundle.
- Surface_bundle_over_the_circle type AnatomicalStructure.
- Surface_bundle_over_the_circle type Bundle.
- Surface_bundle_over_the_circle comment "In mathematics, a surface bundle over the circle is a fiber bundle with base space a circle, and with fiber space a surface. Therefore the total space has dimension 2 + 1 = 3. In general, fiber bundles over the circle are a special case of mapping tori.Here is the construction: take the Cartesian product of a surface with the unit interval. Glue the two copies of the surface, on the boundary, by some homeomorphism. This homeomorphism is called the monodromy of the surface bundle.".
- Surface_bundle_over_the_circle label "Surface bundle over the circle".
- Surface_bundle_over_the_circle sameAs Q7645953.
- Surface_bundle_over_the_circle sameAs m.06dybb.
- Surface_bundle_over_the_circle sameAs Q7645953.
- Surface_bundle_over_the_circle wasDerivedFrom Surface_bundle_over_the_circle?oldid=342664314.
- Surface_bundle_over_the_circle isPrimaryTopicOf Surface_bundle_over_the_circle.