[Note: All manifolds are assumed to be Hausdorff and paracompact, and to have a countable base.]
Around 1969, R. Kirby & L. Siebenmann first showed that there exist topological manifolds that admit no PL structure.
It was since shown that there could exist a manifold triangulated as a simplicial complex but with a non-PL triangulation. (E.g., the double suspension of a triangulated nontrivial homology 3-sphere gives a non-PL triangulation of S^5. Of course, S^5 admits other triangulations that are PL.)
QUESTION: Do there exist topological manifolds that admit no triangulation (PL or not) whatsoever??? In any case, what is known about the range of dimensions for which this may be possible?
References to the literature would be appreciated.
Dr. Daniel Asimov Senior Research Scientist
Mail Stop T27A-1 NASA Ames Research Center Moffett Field, CA 94035-1000
firstname.lastname@example.org (415) 604-4799 w (415) 604-3957 fax