In mathematics, more specifically in geometric topology, the Kirby–Siebenmann class is an obstruction for topological manifolds to allow a "PL"-structure.
The KS-class.
For a topological manifold "M", the Kirby–Siebenmann class formula_1 is an element of the fourth cohomology group of "M" that vanishes if "M" admits a piecewise linear structure. 
It is the only such obstruction, which can be phrased as the weak equivalence formula_2 of "TOP/PL" with an Eilenberg–MacLane space. 
The Kirby-Siebenmann class can be used to prove the existence of topological manifolds that do not admit a PL-structure. Concrete examples of such manifolds are formula_3, where formula_4 stands for Freedman's E8 manifold.
The class is named after Robion Kirby and Larry Siebenmann, who developed the theory of topological and "PL"-manifolds.
References.
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