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Theorem in geometry
In geometry, Thurston's geometrization theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular
Hyperbolization_theorem
Mathematical space
conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture
3-manifold
Topics referred to by the same term
In geometry, geometrization theorem may refer to Thurston's hyperbolization theorem for Haken 3-manifolds Thurston's geometrization conjecture proved
Geometrization_theorem
American mathematician (1946–2012)
his celebrated hyperbolic Dehn surgery theorem. To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important
William_Thurston
Three dimensional analogue of uniformization conjecture
conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture
Geometrization_conjecture
On when a sequence of quasi-Fuchsian groups have a convergent subsequence
in Thurston's proof of the hyperbolization theorem for the case of manifolds that fiber over the circle. By Bers's theorem, quasi-Fuchsian groups (of
Double_limit_theorem
Space where every point locally resembles a hyperbolic space
their respective manifolds. Hyperbolic 3-manifold Hyperbolic space Hyperbolization theorem Margulis lemma Normally hyperbolic invariant manifold Kapovich
Hyperbolic_manifold
Operation combining two oriented knots
turn into 3-manifold theory. The JSJ decomposition and Thurston's hyperbolization theorem reduces the study of knots in the 3-sphere to the study of various
Knot_(mathematics)
Part of the mathematical subject of group theory
provides substantial shortcuts in modern proofs of Thurston's Hyperbolization Theorem for Haken 3-manifolds. Similarly, R-trees play a key role in the
Bass–Serre_theory
further into the mainstream. In the late 1970s William Thurston's hyperbolization theorem introduced the theory of hyperbolic 3-manifolds into knot theory
History_of_knot_theory
Study of mathematical knots
introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Many knots were shown to be hyperbolic knots, enabling the use
Knot_theory
Tait flyping conjecture in 1991. Menasco, applying Thurston's hyperbolization theorem for Haken manifolds, showed that any prime, non-split alternating
Alternating_knot
Mathematics concept
manifolds. The hierarchy played a crucial role in William Thurston's hyperbolization theorem for Haken manifolds, part of his revolutionary geometrization program
Haken_manifold
Conjecture pertaining to finite covers of 3-manifold subfields
the fact that any of these conjectures, combined with Thurston's hyperbolization theorem, would imply the geometrization conjecture. However, in practice
Virtually_fibered_conjecture
provides substantial shortcuts in modern proofs of Thurston's hyperbolization theorem for Haken 3-manifolds. Similarly, R {\displaystyle \mathbb {R}
Rips_machine
Mathematics timeline
2018. Gallier, Jean; Xu, Dianna (2013). A Guide to the Classification Theorem for Compact Surfaces. Springer Science & Business Media. p. 156. ISBN 9783642343643
Timeline_of_manifolds
American mathematician
Riemannian hyperbolization procedure developed by Ontaneda in a series of papers, which is a smooth version of the strict hyperbolization procedure introduced
Pedro_Ontaneda
Gruyter, p. 294, ISBN 9783110808056. Otal, Jean-Pierre (2001), The hyperbolization theorem for fibered 3-manifolds, Contemporary Mathematics, vol. 7, American
Atoroidal
American mathematician (born 1949)
with Tadeusz Januszkiewicz [pl] and Ruth Charney, he established the "hyperbolization" method for using nonpositive curvature to construct aspherical manifolds
Michael_W._Davis
1992 book by Underwood Dudley
Fermat's Last Theorem, non-Euclidean geometry and the parallel postulate, the golden ratio, perfect numbers, the four color theorem, advocacy for duodecimal
Mathematical_Cranks
Elementary particle involved with rest mass
also seemed to predict known massive particles as massless. Goldstone's theorem, relating to continuous symmetries within some theories, also appeared
Higgs_boson
Plane curve: conic section
{m_{1}}{m_{2}}}\ .} Analogous to the inscribed angle theorem for circles one gets the Inscribed angle theorem for hyperbolas—For four points P i = ( x i , y
Hyperbola
Italian-American physicist (1901–1954)
behaves as if it were a Euclidean space. Fermi submitted his thesis, "A theorem on probability and some of its applications" (Un teorema di calcolo delle
Enrico_Fermi
Dutch computer scientist (1930–2002)
maintenance. A more successful effort was the Standard Proof for Pythagoras' Theorem, that replaced the more than 100 incompatible existing proofs. Dijkstra
Edsger_W._Dijkstra
Dutch mathematician and physicist (1629–1695)
Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli (Theorems on the quadrature of the hyperbola, ellipse, and circle)
Christiaan_Huygens
Ancient Greek geometer and astronomer (c. 240–190 BC)
'about diorismic theorems', which Halley translated as “de theorematis ad determinationem pertinentibus,” and Heath as “theorems involving determinations
Apollonius_of_Perga
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
Boy/Male
Indian
A prophets name
Girl/Female
Tamil
Wish, Desire
Boy/Male
Tamil
Sarvodaya | ஸரà¯à®µà¯‹à®¤à®¯à®¾
Welfare of all, Universal uplift and progress of all
Girl/Female
Latin
Little precious jewel.
Boy/Male
Indian, Sanskrit
Lord Shiva
Boy/Male
Indian
Without a Companion; Without an Equal
Boy/Male
Indian, Punjabi, Sikh
Taking the Support of Truth
Boy/Male
Indian, Telugu
Speak Truth
Boy/Male
Muslim
A tree, Sincere
Boy/Male
Hindu, Indian
Gift from God
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
HYPERBOLIZATION THEOREM
v. t.
To formulate into a theorem.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
a.
Theorematic.
n.
A numerical coefficient in any particular case of the binomial theorem.
a.
Alt. of Theorematical
n.
A statement of a principle to be demonstrated.
n.
One who constructs theorems.