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Topic: Non-PL Triangulation of Manifolds -- What's the Latest???
Replies: 3   Last Post: Jul 15, 1996 10:42 AM

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Daniel A. Asimov

Posts: 101
Registered: 12/3/04
Non-PL Triangulation of Manifolds -- What's the Latest???
Posted: Jul 10, 1996 4:25 PM
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[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

asimov@nas.nasa.gov
(415) 604-4799 w
(415) 604-3957 fax







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