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  "body": "\n## Summary\n\nThe Kirby–Siebenmann class of a topological manifold $M$ is a cohomology class $\\operatorname{ks}(M) \\in H^4(M; \\Z/2)$.\nIt is the obstruction to putting a piecewise linear structure on $M \\times \\R$, and, when $\\dim M \\ge 5$, on $M$ itself.\nIt shows that topological manifolds and piecewise linear manifolds really differ.\nIn dimension $4$, a manifold whose class is nonzero, such as the $E_8$ manifold, has no smooth structure.\n\n## Explanations\n\n### L1 human\n\nSome topological manifolds can be cut into simplices in a way that makes them piecewise linear, and some cannot.\nKirby and Siebenmann found a single test for this, in the form of one cohomology class with coefficients in $\\Z/2$.\nIf the class is nonzero, no piecewise linear or smooth structure exists.\nIn dimensions five and higher, a zero class means that a piecewise linear structure does exist.\n",
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