Timeline for Two natural maps asssociated with the nerve of a cover
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2016 at 9:31 | comment | added | Roberto Frigerio | A reference for the map I was mentioning is e.g. Hatcher's book "Algebraic Topoology", Section 4.G (the book is available here: math.cornell.edu/~hatcher/AT/AT.pdf ). I also found a reference to this map in Spanier's book "Algebraic topology", in the exerxises at page 152. | |
| Apr 15, 2016 at 10:13 | comment | added | Sebastian Goette | If you have a nice reference for the first map, please tell me. I am using it in a different context to smooth out a piecewise smooth object defined on the nerve. | |
| Apr 15, 2016 at 8:15 | comment | added | Roberto Frigerio | Hi Denis! The reasons why I am taking sheaves rather than presheaves are two. The first one is that this question arises from the proof of the theorem on amenable coverings in the paper "Foundations of the theory of bounded cohomology", where the problem was posed exactly in these terms. The second one is that without sheafifying the rows of the double complex are not exact, so you need indeed a spectral sequence rather than simply a double complex, and since I am not at ease with spectral sequences I was quite happy about that. | |
| Apr 14, 2016 at 15:21 | comment | added | Denis Nardin | Why are you sheavifying in the construction of the double complex? I think that the spectral sequences converges to $H^*(X)$ even if you don't do that (also I find it funny that I never heard of the "well-known" first map and I consider the second map a fairly natural one arising from the Mayer-Vietoris spectral sequence) | |
| Apr 14, 2016 at 14:46 | history | asked | Roberto Frigerio | CC BY-SA 3.0 |