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- Geometric_topology_(object) abstract "In mathematics, the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume. Convergence in this topology is a crucial ingredient of hyperbolic Dehn surgery, a fundamental tool in the theory of hyperbolic 3-manifolds. The following is a definition due to Troels Jorgensen: A sequence in H converges to M in H if there are a sequence of positive real numbers converging to 0, and a sequence of -bi-Lipschitz diffeomorphisms where the domains and ranges of the maps are the -thick parts of either the 's or M. There is an alternate definition due to Mikhail Gromov. Gromov's topology utilizes the Gromov-Hausdorff metric and is defined on pointed hyperbolic 3-manifolds. One essentially considers better and better bi-Lipschitz homeomorphisms on larger and larger balls. This results in the same notion of convergence as above as the thick part is always connected; thus, a large ball will eventually encompass all of the thick part. As a further refinement, Gromov's metric can also be defined on framed hyperbolic 3-manifolds. This gives nothing new but this space can be explicitly identified with torsion-free Kleinian groups with the Chabauty topology.".
- Geometric_topology_(object) wikiPageExternalLink gt3m.
- Geometric_topology_(object) wikiPageID "4459380".
- Geometric_topology_(object) wikiPageRevisionID "590185733".
- Geometric_topology_(object) hasPhotoCollection Geometric_topology_(object).
- Geometric_topology_(object) subject Category:3-manifolds.
- Geometric_topology_(object) subject Category:Hyperbolic_geometry.
- Geometric_topology_(object) subject Category:Topological_spaces.
- Geometric_topology_(object) type Abstraction100002137.
- Geometric_topology_(object) type Attribute100024264.
- Geometric_topology_(object) type MathematicalSpace108001685.
- Geometric_topology_(object) type Set107999699.
- Geometric_topology_(object) type Space100028651.
- Geometric_topology_(object) type TopologicalSpaces.
- Geometric_topology_(object) comment "In mathematics, the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume. Convergence in this topology is a crucial ingredient of hyperbolic Dehn surgery, a fundamental tool in the theory of hyperbolic 3-manifolds.".
- Geometric_topology_(object) label "Geometric topology (object)".
- Geometric_topology_(object) sameAs m.0c3mc7.
- Geometric_topology_(object) sameAs Q5535500.
- Geometric_topology_(object) sameAs Q5535500.
- Geometric_topology_(object) sameAs Geometric_topology_(object).
- Geometric_topology_(object) wasDerivedFrom Geometric_topology_(object)?oldid=590185733.
- Geometric_topology_(object) isPrimaryTopicOf Geometric_topology_(object).