Timeline for When are (finite) simplicial complexes (smooth) manifolds?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2013 at 16:39 | comment | added | Dylan Wilson | Any manifold with boundary has the homotopy type of a manifold without boundary, so you don't need that requirement... | |
| Jul 28, 2011 at 3:42 | answer | added | Ben Wieland | timeline score: 4 | |
| Jul 27, 2011 at 17:35 | history | edited | Ryan Budney |
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| Jul 27, 2011 at 17:10 | comment | added | Ryan Budney | All finite simplicial complexes have the homotopy-type of manifolds, provided you allow the manifolds to have boundary. The proof is given by embedding the simplicial complex in a suitably high-dimensional manifold (say Euclidean space) and then taking a smooth regular neighbourhood of the complex. The regular neighbourhood has the same homotopy-type and it's a smooth manifold. | |
| Jul 27, 2011 at 14:32 | answer | added | Igor Rivin | timeline score: 14 | |
| Jul 27, 2011 at 14:10 | comment | added | Lennart Meier | There is not really a big difference between (b) and (d) since every compact differentiable manifold is a real algebraic variety as cited in aimsciences.org/journals/pdfs.jsp?paperID=2431&mode=full [a result due to Nash and Tognoli] | |
| Jul 27, 2011 at 14:06 | answer | added | Mikael Vejdemo-Johansson | timeline score: 5 | |
| Jul 27, 2011 at 13:43 | history | asked | Markus Ulke | CC BY-SA 3.0 |