Timeline for Does compactly supported cohomology make sense for cosimplicial spaces?
Current License: CC BY-SA 3.0
11 events
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| Nov 23, 2013 at 10:26 | comment | added | John Salvatierrez | @FernandoMuro: OK, let's say I have a cosimplicial object in simplicial complexes, is there a functioning theory of compactly supported cohomology in this case? (I'm just trying to understand where the real obstacle lies and then work from there) | |
| Nov 23, 2013 at 5:21 | comment | added | Fernando Muro | Sorry, I meant simplicial maps between simplicial * complexes* | |
| Nov 22, 2013 at 23:38 | comment | added | John Salvatierrez | @FernandoMuro: in your comment your mentioned that locally finite chains were functorial only with respect to simplicial maps, that's why I'm asking. | |
| Nov 22, 2013 at 23:32 | comment | added | Fernando Muro | in which way are cosimplicial spaces a problem over cosimplicial simplicial sets? | |
| Nov 22, 2013 at 22:41 | comment | added | John Salvatierrez | @FernandoMuro: Is the problem in your suggestion that we are working with cosimplicial spaces rather than cosimplicial-simplicial sets? I'd be interested to know whether a theory of compactly supported cohomology (or BM homology) for such (appropriately nice/finite) gadgets existed. | |
| Nov 22, 2013 at 18:40 | comment | added | Fernando Muro | I don't really have any nice suggestion. I'd like to be able to say something like: take levelwise the complex of locally finite chains, in an ideal world this would give rise to a cosimplicial chain complex, then totalize, and consider the homology of that complex. The problem is that I think that assuming each space to be a locally compact polyhedron doesn't help that much because the chain complex of locally finite chains I think it's only functorial with respect to simplicial maps, so you would have to try to take many compatible simplicial approximations. Who knows... | |
| Nov 21, 2013 at 18:55 | comment | added | John Salvatierrez | Do you have any suggestions? I was hoping people smarter than me had already thought about it, that's why I asked. In general, is there a good place to read about cosimplicial spaces? What about simplicial-cosimplicial ones? | |
| Nov 21, 2013 at 18:46 | comment | added | Fernando Muro | John, probably you can, but maybe you want your definition to satisfy some properties, and hopefully that would lead you to an appropriate definition. | |
| Nov 21, 2013 at 18:43 | comment | added | John Salvatierrez | @FernandoMuro: OK, let's say I have a cosimiplicial space, which at each level is homeomorphic to a locally finite simplicial complex. Can I define BM homology for that? | |
| Nov 21, 2013 at 18:11 | comment | added | Fernando Muro | I find this question somewhat unclear, the BM-homology is defined for locally finite simplicial complexes, right? Not even for simplicial sets in general. | |
| Nov 21, 2013 at 10:24 | history | asked | John Salvatierrez | CC BY-SA 3.0 |