Timeline for Is a functor which is a sheaf for open covers and finite closed covers automatically a sheaf for covers by simplices?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2012 at 17:51 | comment | added | Peter Arndt | No, I haven't thought about it for two years. Do you have an idea? | |
| May 9, 2012 at 2:45 | comment | added | David Carchedi | @Peter: Have you made any progress with this? | |
| Apr 26, 2010 at 22:00 | comment | added | Peter Arndt | One thing that confuses me in the general case are scenarios of the following kind: Put a triangle into R^3, placing its base onto the x-axis, then rotate it around the x-axis. This gives uncountably many simplices all coinciding at one face, which occur for example in the simplicial set Sing(R^3). I have no idea how to get the sheaf property for such arrangements... | |
| Apr 25, 2010 at 18:32 | comment | added | Torsten Ekedahl | I only lconsidered a few examples but it seems that looking at the intersection pattern of the simplices of the barycentric subdivision (and using the sheaf property for closed coverings) would suffice. I know that there are situations where there is a difference between the first and second barycentric subdivisions so one might have to go to the simplices in the second subdivision. This would handle simplicial sets with only a finite number of non-degenerate simplices. The general case could then possibly be handled by using the open covering property using stars of finite subcomplexes. | |
| Apr 25, 2010 at 17:25 | comment | added | Peter Arndt | Ok, I tried ... | |
| Apr 25, 2010 at 17:24 | history | edited | Peter Arndt | CC BY-SA 2.5 |
edited title
|
| Apr 25, 2010 at 2:21 | comment | added | Theo Johnson-Freyd | Please try to give a more descriptive title. You have something like 200 or 250 characters for the title --- more than a tweet. For example, this comment fits in a title on MathOverflow. | |
| Apr 24, 2010 at 21:55 | history | edited | Peter Arndt | CC BY-SA 2.5 |
added 279 characters in body; added 61 characters in body
|
| Apr 24, 2010 at 21:46 | history | asked | Peter Arndt | CC BY-SA 2.5 |