Piecewise linear manifold

Summary

A piecewise linear manifold, or PL manifold, is a topological manifold together with an atlas whose changes of chart are piecewise linear. Equivalently, it is a manifold given with a triangulation in which the neighbourhood of every vertex is a standard piecewise linear ball. PL manifolds sit between topological and smooth manifolds. They are the natural setting for combinatorial methods such as handle moves, regular neighbourhoods and simple homotopy theory.