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2π theorem

Index 2π theorem

In mathematics, the 2 theorem of Gromov and Thurston states a sufficient condition for Dehn filling on a cusped hyperbolic 3-manifold to result in a negatively curved 3-manifold. [1]

16 relations: Atoroidal, Colin Adams (mathematician), Fundamental group, Geometrization conjecture, Geometry & Topology, Horosphere, Hyperbolic 3-manifold, Hyperbolic Dehn surgery, Hyperbolic group, Inventiones Mathematicae, Mathematics, Mikhail Leonidovich Gromov, Prime decomposition (3-manifold), Seifert fiber space, Topology (journal), William Thurston.

Atoroidal

In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus.

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Colin Adams (mathematician)

Colin Conrad Adams (born October 13, 1956) is a mathematician primarily working in the areas of hyperbolic 3-manifolds and knot theory.

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Fundamental group

In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

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Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them.

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Geometry & Topology

Geometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications.

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Horosphere

In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic ''n''-space.

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Hyperbolic 3-manifold

In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1.

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Hyperbolic Dehn surgery

In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold.

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Hyperbolic group

In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.

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Inventiones Mathematicae

Inventiones Mathematicae is a mathematical journal published monthly by Springer Science+Business Media.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Mikhail Leonidovich Gromov

Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.

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Prime decomposition (3-manifold)

In mathematics, the prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite collection of prime 3-manifolds.

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Seifert fiber space

A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles.

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Topology (journal)

Topology was a peer-reviewed mathematical journal covering topology and geometry.

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William Thurston

William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician.

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References

[1] https://en.wikipedia.org/wiki/2π_theorem

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