Kirby–Siebenmann class
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 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 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, where 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.
