Worth noting here that (checking Wikipedia) "triangulation" here is being used in a weaker sense than the usual piecewise-linear triangulation. (Apparently, be

Worth noting here that (checking Wikipedia) "triangulation" here is being used in a weaker sense than the usual piecewise-linear triangulation. (Apparently, being homeomorphic to a simplicial complex doesn't mean admitting a PL structure! Not news to any topologists, I guess, but news to me.) If we restrict to that narrower notion of triangulation, it was already known how to build high-dimensional manifolds with no triangulation.