Timeline for A category of manifolds that includes Polygonal domains
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2012 at 6:15 | comment | added | Mariano Suárez-Álvarez | What goes wrong if one defines a polyfold (excuse the silly neologism) as, say, a Hausdorff 2nd countable space which is locally modelled on closed polyhedral cones just as manifolds with corners are locally modeled on orthants? | |
| Aug 2, 2012 at 17:19 | comment | added | shuhalo | yes, I meant not manifolds with corners. --- It seems that even manifolds with corners are only a very small subbranch that has barely been investigated and canonicalized. | |
| Aug 2, 2012 at 17:18 | history | edited | shuhalo | CC BY-SA 3.0 |
correction
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| Aug 2, 2012 at 15:11 | comment | added | Misha | You can also use the category of PL manifolds with boundary or topological submanifolds with boundary. It all depends on the equivalence relation you want to have on your domains (or sheaves of functions that you would like to consider). If you allow that a (closed) quadrant is isomorphic to a half-plane, then PL or TOP suffice. If not, you have to use stratified spaces as in Rafe's answer. Also, by "polygon" you probably mean "polyhedron" (otherwise $n=2$). | |
| Aug 2, 2012 at 14:59 | answer | added | Rafe Mazzeo | timeline score: 8 | |
| Aug 2, 2012 at 14:45 | comment | added | Andrew Stacey | Do you mean "are not submanifolds with corners in general"? As for the actual question, there are plenty of categories of generalised smooth spaces that would include these but I guess you want something a bit smaller. What properties do you want for your category of "manifolds"? | |
| Aug 2, 2012 at 14:17 | history | asked | shuhalo | CC BY-SA 3.0 |