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Foliation

In mathematics, a p-dimensional foliation is a partition of a manifold into submanifolds, all of the same dimension p, locally modeled on the decomposition of Rn into the p-dimensional planes cut out by the equations x p + 1 = a p + 1 , … , x n = a n {\displaystyle x_{p+1}=a_{p+1},\ldots ,x_{n}=a_{n}} . The submanifolds are called the leaves of the…

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Overview

Foliated charts and atlases

Foliation definitions

Holonomy

Examples

Foliations and integrability

Existence of foliations

Advanced semantic analysis

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Map overview Semantic statistics

Foliation

Nodes107
Edges106
Triples72
Avg. degree1.98
Density0.018692
Components1

How this topic connects Entity context

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Foliation

Top relations

related to Foliated bundles · 10
Foliation → Because, Cr, If, In, Let, Poincaré, Suppose, That, The, This
related to Foliation definitions · 7
Foliation → Cr, Definition, Every, Lα, Rn, Several, The
see also · 7
Foliation → Concept, G-structure, Generalization, Lamination, Partitioned, Structure, Taut
related to Bundles · 6
Foliation → Another, Bf, Fb, G-bundles, Given, Homeo
related to Foliated charts and atlases · 6
Foliation → If J1, In, J1, Ji, Jn, Rn
related to Foliations and integrability · 6
Foliation → Frobenius, GL, Lie, One, There, This
related to Holonomy · 6
Foliation → As, Holonomy, If, Intuitively, Let, This
related to Reeb foliations · 5
Foliation → Define, Dn, Sn, This, Z-actions
related to Submersions · 4
Foliation → An, Fiber, If Mn, Nq
related to Lie group actions · 3
Foliation → If, Let, Lie

Important terminology Word statistics

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Important terminology

displaystyle foliated mathcal leaves manifold one leaf foliations bundle flow atlas s1 cr called compact transverse class torus connected definition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Foliationis apartition of a manifold into submanifolds0.90text
Foliationis asubmersion allowing the followingDefinition0.90text
Foliationrelated to BundlesFb0.60section
Foliationrelated to BundlesAnother0.60section
Foliationrelated to BundlesBf0.60section
Foliationrelated to BundlesG-bundles0.60section
Foliationrelated to BundlesHomeo0.60section
Foliationrelated to BundlesGiven0.60section
Foliationrelated to CoveringsIf0.60section
Foliationrelated to CoveringsMore0.60section
Foliationrelated to Existence of foliationsHaefliger0.60section
Foliationrelated to Existence of foliationsThurston0.60section

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    Min side: 3
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