High Quality Content by WIKIPEDIA articles! 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. An isomorphism of PL manifolds is called a PL homeomorphism. PL, or more precisely PDIFF, sits between DIFF (the category of smooth manifolds) and TOP (the category of topological manifolds): it is categorically "better behaved" than DIFF – for example, the Generalized Poincare conjecture is true in PL, but not in DIFF – but is "worse behaved" than TOP, as elaborated in surgery theory.

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