Inmathematics, more specifically in geometric topology, the Kirby–Siebenmann class is an obstruction for topological manifolds to allow a PL-structure.[1]
For a topological manifold M, the Kirby–Siebenmann class is an element of the fourth cohomology groupofM that vanishes if M admits a piecewise linear structure.
It is the only such obstruction, which can be phrased as the weak equivalence ofTOP/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.[2] Concrete examples of such manifolds are , where stands for Freedman's E8 manifold.[3]
The class is named after Robion Kirby and Larry Siebenmann, who developed the theory of topological and PL-manifolds.
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