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Piecewise linear manifold

In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise linear functions. This is slightly stronger than the topological notion of a triangulation. An isomorphism…

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Overview

Mathematics
Topological manifold
Atlas Atlas (topology)
Chart Chart (topology)
Piecewise linear functions Piecewise linear function
Triangulation Triangulation (topology)
Isomorphism

Relation to other categories of manifolds

Smooth manifolds Smooth manifold
Generalized Poincaré conjecture
Surgery theory
Whitehead 1940 Piecewise linear manifold
Smooth structure
Piecewise-smooth manifolds Piecewise-smooth manifold
Cones Cone (topology)
Homotopy sphere
H-cobordism
Exotic spheres Exotic sphere
Hauptvermutung
Kirby–Siebenmann class
Obstruction Obstruction theory
Real-algebraic sets Real algebraic set
Combinatorial manifold
Simplicial complexes
Digital manifold
Digital topology

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Map overview Semantic statistics

Piecewise linear manifold

Nodes28

Edges27

Triples2

Avg. degree1.93

Density0.071429

Components1

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Piecewise linear manifold

Top relations

related to Combinatorial manifolds and digital manifolds · 2

Piecewise linear manifold → It, See

Important terminology Word statistics

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Important terminology

pl manifold manifolds topological structure piecewise smooth linear one sets combinatorial digital triangulation diff category way defined means functions real

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Piecewise linear manifold	related to Combinatorial manifolds and digital manifolds	It	0.60	section
Piecewise linear manifold	related to Combinatorial manifolds and digital manifolds	See	0.60	section

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Min side: 3

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