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Process in mathematics of decomposing a topological space
mathematical field of topology, the JSJ decomposition, also known as the toral decomposition, is a decomposition of a 3-manifold into a finite number
JSJ_decomposition
Operation combining two oriented knots
study of their complements, and in turn into 3-manifold theory. The JSJ decomposition and Thurston's hyperbolization theorem reduces the study of knots
Knot_(mathematics)
Topics referred to by the same term
JSJ may refer to: IATA code for Jiansanjiang Airport JSJ decomposition, a process in mathematics of decomposing a topological space This disambiguation
JSJ
Mathematical space
embedding of either a torus or an annulus The JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following
3-manifold
Three dimensional analogue of uniformization conjecture
the JSJ decomposition, which is not quite the same as the decomposition in the geometrization conjecture, because some of the pieces in the JSJ decomposition
Geometrization_conjecture
Topics referred to by the same term
group decomposition, used to analyse the structure of Lie groups and associated objects Manifold decomposition, decomposition of manifolds JSJ decomposition
Decomposition (disambiguation)
Decomposition_(disambiguation)
Part of the mathematical subject of group theory
The theory of JSJ-decompositions for finitely presented groups. This theory was motivated by the classic notion of JSJ decomposition in 3-manifold topology
Bass–Serre_theory
Type of mathematical knot
examples where the decomposition is not unique. With a suitably enhanced notion of satellite operation called splicing, the JSJ decomposition gives a proper
Satellite_knot
Israeli mathematician
notion of a JSJ-decomposition for word-hyperbolic groups, motivated by the notion of a JSJ decomposition for 3-manifolds. A JSJ-decomposition is a representation
Zlil_Sela
Conjecture in knot theory relating quantum invariants and hyperbolic geometry
defined as follows. By the JSJ decomposition, the complement S 3 ∖ K {\displaystyle S^{3}\backslash K} may be uniquely decomposed into a system of tori S
Volume_conjecture
Area in mathematics devoted to the study of finitely generated groups
"Cyclic splittings of finitely presented groups and the canonical JSJ decomposition". Annals of Mathematics. Second Series. 146 (1): 53–109. doi:10.2307/2951832
Geometric_group_theory
Loop theorem (aka the Disk theorem) Sphere theorem Haken manifold JSJ decomposition Branched surface Lamination Examples 3-sphere Torus bundles Surface
List of geometric topology topics
List_of_geometric_topology_topics
American mathematician
working primarily in low-dimensional topology. He is the "S" in JSJ decomposition. He graduated from Stuyvesant High School in 1962, before earning
Peter_Shalen
Interlinked multi-loop construction where cutting one loop frees all the others
interestingly, a canonical geometric decomposition in terms of satellite-sum and satellite-tie, which is simpler than JSJ-decomposition, for Brunnian links, was developed
Brunnian_link
Subfield of mathematical topology
present the JSJ decomposition has not been implemented algorithmically in computer software. Neither has the compression-body decomposition. There are
Computational_topology
1907–1935 William Jaco, mathematician; known for his role in the JSJ decomposition theorem M. Eric Johnson, dean of the Owen Graduate School of Management
List of Pennsylvania State University alumni
List_of_Pennsylvania_State_University_alumni
Israeli mathematician of Latvian origin (1948–2024)
"Cyclic splittings of finitely presented groups and the canonical JSJ decomposition". Annals of Mathematics. 2. 146 (1): 53–109. doi:10.2307/2951832.
Eliyahu_Rips
Women's Army Corps officer William Jaco, mathematician; discovered the JSJ decomposition George Judge, economist Subhash Kak, computer scientist and public
List of Oklahoma State University people
List_of_Oklahoma_State_University_people
Limit groups over free groups
which Rips machine techniques can be used Limit groups admit abelian JSJ decompositions Limit groups over a free group of fixed rank form a finite diagram
Limit_group
either a Solv manifold, a manifold having only Seifert pieces in its JSJ decomposition, or connect sums of the previous two categories. From this perspective
Graph_manifold
British mathematician
infinite cyclic group. This allowed Bowditch to produce a theory of JSJ decomposition for word-hyperbolic groups that was more canonical and more general
Brian_Bowditch
Characterizes homeomorphisms of a compact orientable surface
these tori to yield pieces that each have geometric structures (the JSJ decomposition); If g is pseudo-Anosov, then Mg has a hyperbolic (i.e. H3) structure
Nielsen–Thurston classification
Nielsen–Thurston_classification
Mathematical property
as well as 3-manifold groups obtained by some connected sum and JSJ decomposition constructions. For every n ≥ 1 {\displaystyle n\geq 1} the Baumslag–Solitar
Howson_property
depending only on S. In general, it is known, as a consequence of the JSJ-decomposition theory for word-hyperbolic groups, that if 1 → H → G → Q → 1 {\displaystyle
Cannon–Thurston_map
American mathematician
mathematician who is known for his role in the Jaco–Shalen–Johannson decomposition theorem and efficient triangulations of 3-manifolds. He retired from
William_Jaco
British mathematician
accessibility of discrete groups, groups acting on graphs and trees, JSJ-decompositions, the topology of 3-manifolds and the structure of their fundamental
Martin_Dunwoody
for (torsion-free) word-hyperbolic groups, Sela's version of the JSJ-decomposition theory and the work of Sela on the Tarski Conjecture for free groups
Rips_machine
Mathematics textbook
cutting along incompressible surfaces can be used to construct the JSJ decomposition of a manifold. This chapter also includes material on Seifert fiber
Introduction_to_3-Manifolds
theory) Doob decomposition theorem (stochastic processes) Doob's martingale convergence theorems (stochastic processes) Doob–Meyer decomposition theorem (stochastic
List_of_theorems
The Digital Morphological Sampling Theorem, (with X. Zhuang, C. Lin, and J.S.J. Lee), IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume
Robert_Haralick
JSJ DECOMPOSITION
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Girl/Female
Hindu
Led forward, Conducted, Advanced, Promoted, Pure water
Girl/Female
Hindu, Indian, Kannada, Sanskrit, Tamil
Calm
Boy/Male
Hindu
Wish
Girl/Female
Tamil
Keeritika | கிரீதீகா
Boy/Male
Arabic, Muslim
Friend of God
Boy/Male
Hindu
Boy/Male
Hindu, Indian, Marathi
The Eye
Girl/Female
English American French
Derived from Lacey which is a French Nobleman's surname brought to British Isles after Norman...
Male
Yiddish
(×ַבְרוּ×) Yiddish form of Hebrew Avraham, AVRUM means "father of a multitude."Â
Surname or Lastname
English and Scottish
English and Scottish : patronymic from Hugh.
JSJ DECOMPOSITION
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JSJ DECOMPOSITION
n.
A white crystalline aldehyde having a burning taste and characteristic odor of vanilla. It is extracted from vanilla pods, and is also obtained by the decomposition of coniferin, and by the oxidation of eugenol.
n.
A white crystalline substance obtained by the decomposition of saponin.
n.
One of the gaseous or volatile decomposition products of the xanthates, and probably identical with carbon disulphide.
n.
A phenol alcohol obtained, by the decomposition of salicin, as a white crystalline substance; -- called also hydroxy-benzyl alcohol.
n.
A crystalline nitrogenous substance, formed in the decomposition of creatin (one of the constituents of muscle tissue). Chemically, it is methyl glycocoll.
n.
An alkaloid obtained as a yellow amorphous substance by the decomposition of veratrine.
a.
Pertaining to, derived from, or designating, an acid obtained from a lichen (Cetraria vulpina) as a yellow or red crystalline substance which on decomposition yields pulvinic acid.
n.
A body occurring in small quantity in the juices of muscle, in the lungs, and elsewhere, but especially in the bile, where it is found as a component part of taurocholic acid, from which it can be prepared by decomposition of the acid. It crystallizes in colorless, regular six-sided prisms, and is especially characterized by containing both nitrogen and sulphur, being chemically amido-isethionic acid, C2H7NSO3.
n.
A hypothetical radical, SO4, regarded as forming the acid or negative constituent of sulphuric acid and the sulphates in electrolytic decomposition; -- so called in accordance with the binary theory of salts.
n.
A glucoside resembling, but distinct from, quercitrin. Rutin is found in the leaves of the rue (Ruta graveolens) and other plants, and obtained as a bitter yellow crystalline substance which yields quercitin on decomposition.
n.
The chemical basis of sponge tissue, a nitrogenous, hornlike substance which on decomposition with sulphuric acid yields leucin and glycocoll.
n.
A white crystalline substance having a sweet taste and a hyacinthlike odor, obtained by the decomposition of styracin; -- properly called cinnamic, / styryl, alcohol.
n.
A body identical with indigo blue, occasionally found in the urine in degeneration of the kidneys. It is readily formed by oxidation or decomposition of indican.
a.
Pertaining to, or obtained from, grapes; specifically, designating an organic acid, C7H8O3 (also called pyrotritartaric acid), obtained as a white crystalline substance by the decomposition of tartaric and pyrotartaric acids.
n.
The act, process, or result, of soap making; conversion into soap; specifically (Chem.), the decomposition of fats and other ethereal salts by alkalies; as, the saponification of ethyl acetate.
n.
The act or process of resolving the constituent parts of a compound body or substance into its elementary parts; separation into constituent part; analysis; the decay or dissolution consequent on the removal or alteration of some of the ingredients of a compound; disintegration; as, the decomposition of wood, rocks, etc.
n.
A white crystalline nitrogenous substance present in small amount in the pancreas and spleen, and formed in large quantity from the decomposition of proteid matter by various means, -- as by pancreatic digestion, by putrefaction as of cheese, by the action of boiling acids, etc. Chemically, it consists of oxyphenol and amidopropionic acid, and by decomposition yields oxybenzoic acid, or some other benzol derivative.
n.
Indigo red, a product of the decomposition, or oxidation, of indican. It is sometimes found in the sediment of pathological urines. It is soluble in ether or alcohol, giving the solution a beautiful red color. Also called indigrubin.
n.
A liquid hydrocarbon obtained by the decomposition of veratric acid, and constituting the dimethyl ether of pyrocatechin.
v. t.
To convert into soap, as tallow or any fat; hence (Chem.), to subject to any similar process, as that which ethereal salts undergo in decomposition; as, to saponify ethyl acetate.