Timeline for If a polyhedron is homeomorphic to a simplex, is it piecewise-linear homeomorphic?
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| Mar 26, 2012 at 23:04 | comment | added | Dmitri Panov | Gerg, I guess we just use two different terms to define the same notion. I agree with you about dimension 7, there is only one PL structure on $S^7$. But dimension $\ge 7$ are different from $<7$, namely, up to dimension 6 every PL manifold admits a unique smooth structure. In particular all these exotic smooth 4-dimensional manifolds have have exotic PL structures. | |
| Mar 26, 2012 at 22:06 | comment | added | Greg Friedman | But the original question isn't about PL diffeomorphic, it's about PL homeomorphic. Are these the same concept in dimension 4? For example, this argument would not work in dimension 7 where a triangulation of an exotic 7-sphere would have to be PL-homeomorphic to the standard sphere by the PL Poincare conjecture. (For that matter, what does "PL diffeomorphic" mean exactly?) | |
| Mar 26, 2012 at 20:25 | vote | accept | Ernest Davis | ||
| Mar 26, 2012 at 20:09 | vote | accept | Ernest Davis | ||
| Mar 26, 2012 at 20:25 | |||||
| Mar 26, 2012 at 18:55 | history | answered | Dmitri Panov | CC BY-SA 3.0 |