Timeline for Simplicial complexes vs. geometric realization of abstract simplicial complexes
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2010 at 16:04 | comment | added | David E Speyer | The error is no more. | |
| May 6, 2010 at 16:01 | comment | added | Robin Chapman | Let's try to orient this surface. Suppose that $abc$ "goes clockwise". Then so do $acd$, $ade$, $bed$, $bce$ and $acb$. So $abc$ goes both clockwise and anticlockwise. :-) | |
| May 6, 2010 at 15:58 | comment | added | David E Speyer | That's an error in Wikipedia. The condition should be that the neighbouring edges are pointing in opposite directions. (Draw a picture.) | |
| May 6, 2010 at 15:55 | comment | added | user4676 | I am totally confused now. A total order $a<b<c<d<e<f$ on $\{a,b,c,d,e,f\}$ gives in particular an orientation of all the $2$-simplices. Now (see Wikipedia on orientability) "Any surface has a triangulation (...) Each triangle is oriented by choosing a direction around the perimeter of the triangle, associating a direction to each edge of the triangle. If this is done in such a way that, when glued together, neighboring edges are pointing in the same direction, then this determines an orientation of the surface. Such a choice is only possible if the surface is orientable,(...)". | |
| May 6, 2010 at 14:27 | history | answered | Robin Chapman | CC BY-SA 2.5 |