Piecewise linear manifold

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In mathematics, a piecewise linear (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.

Smooth manifolds have PL structures, but PL manifolds do not always have smooth structures.

[edit] See also

• Kirby-Siebenmann class
• Hauptvermutung
• simplicial manifold

[edit] References

• Rudyak, Yuli B. (2001). "Piecewise linear structures on topological manifolds". arXiv:math.AT/0105047.