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  "body": "\n## Summary\n\nA piecewise linear manifold, or PL manifold, is a topological manifold together with an atlas whose changes of chart are piecewise linear.\nEquivalently, it is a manifold given with a triangulation in which the neighbourhood of every vertex is a standard piecewise linear ball.\nPL manifolds sit between topological and smooth manifolds.\nThey are the natural setting for combinatorial methods such as handle moves, regular neighbourhoods and simple homotopy theory.\n\n## Explanations\n\n### L1 human\n\nA PL manifold is a manifold built from flat pieces, such as triangles or tetrahedra, glued along faces.\nThe surface of a cube is a PL $2$-sphere: it is made of flat squares, and its corners are no problem.\nMaps between PL manifolds are allowed to bend, but only along flat creases, never in a smooth curve.\nEvery smooth manifold can be given such a flat-pieces structure, but some topological manifolds cannot.\n",
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