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.
- Kirby, Robion C.; Siebenmann, Laurence C. (1977). Foundational Essays on Topological Manifolds, Smoothings, and Triangulations (PDF). Princeton, NJ: Princeton Univ. Pr. ISBN 0-691-08191-3.
- Yuli B. Rudyak. Piecewise linear structures on topological manifolds. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2016.
- Francesco Polizzi. "Example of a triangulable topological manifold which does not admit a PL structure (answer on Mathoverflow)".
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