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2π theorem

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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.


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

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Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

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Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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Christmas traditions

Christmas traditions vary from country to country.

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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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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 (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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New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

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New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

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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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2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

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

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