One of my classmates was telling me that it is an open question whether every 3-manifold can be triangulated. This was rather surprising. He said that the question as far as he remember is settled only for 4-manifold where answer is negative. If this is the case, can somebody shed some light why this problem is so hard?
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closed as off topic by Franz Lemmermeyer, J.C. Ottem, Andrew Stacey, Qiaochu Yuan, S. Carnahan♦ Apr 29 2011 at 10:06 |
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Every $3$-manifold is triangulable. This was proven by Edwin E. Moise in is paper "Affine structure in $3$-manifolds", Annals of Math. 56 (1952). |
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