Timeline for How to compute the cohomology of the general linear group with integral entries
Current License: CC BY-SA 3.0
12 events
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| Jun 25, 2011 at 23:55 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Jun 23, 2011 at 22:41 | answer | added | Ian Agol | timeline score: 2 | |
| Jun 23, 2011 at 21:34 | answer | added | John Rognes | timeline score: 8 | |
| Mar 3, 2011 at 12:30 | history | edited | Hugo Chapdelaine |
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| Mar 3, 2011 at 9:56 | comment | added | François Brunault | About this article of Elbaz-Vincent, Gangl and Soulé, there seems to be a more recent preprint : ihes.fr/~soule/egs.pdf | |
| Mar 3, 2011 at 9:50 | comment | added | François Brunault | @Hugo : See also P. Elbaz-Vincent, H. Gangl et C. Soulé, "Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z" (in French), math.uiuc.edu/K-theory/0581 | |
| Mar 3, 2011 at 1:25 | comment | added | Ralph | @Jim: Soule's paper "The cohomology of $SL_3(\mathbf{Z})$" also contains the integral cohomology of $GL_3(\mathbf{Z}) = SL_3(\mathbf{Z}) \times \mathbf{Z}/2\mathbf{Z}$. | |
| Mar 3, 2011 at 0:42 | comment | added | Jim Conant | Soule has made some integral calculations for $SL_n(\mathbb Z)$ for $n=3,4$, which is not too far away from $GL_n(\mathbb Z)$. | |
| Mar 3, 2011 at 0:34 | comment | added | Ralph | To my knowledge not much is known for general n. There are some results by Ash (see his homepage: www2.bc.edu/~ashav). You also may have a look at the book "Knudson: Homology of Linear Groups". The stable rank ($n = \infty$) has been computed by Borel in the paper "Stable real cohomology of arithmetic groups". | |
| Mar 3, 2011 at 0:00 | comment | added | Theo Buehler | A better candidate for $E$ would certainly be the symmetric space associated to $\operatorname{GL}_{n}(\mathbb{R})$, i.e., the symmetric positive definite matrices. Serre has made extensive calculations of the cohomology of discrete subgroups of Lie groups (e.g. here springerlink.com/content/0171m21753248642), but I think mostly with real coefficients. | |
| Mar 2, 2011 at 23:45 | history | edited | Hugo Chapdelaine | CC BY-SA 2.5 |
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| Mar 2, 2011 at 23:38 | history | asked | Hugo Chapdelaine | CC BY-SA 2.5 |