Timeline for Cohomology of Bott-Samelson varieties?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 8, 2014 at 3:42 | comment | added | Allen Knutson | This is exactly what the original Bott and Samelson paper is about, and you should look at it. (Only later did people even realize that these manifolds are algebraic varieties, much less that they provide resolutions of singularities.) | |
| Jul 4, 2014 at 18:34 | comment | added | Matthias Wendt | The additive structure is completely described by Sasha's comment - additively, the cohomology of the Bott-Samelson variety is the same as for $(\mathbb{P}^1)^{\times n}$. If you are additionally interested in the ring structure of generalized cohomology theories of Bott-Samelson varieties, you might want to check out part 2 of arXiv:0905.1341 of Calmès, Petrov and Zainoulline (as well as the references in there, to the classics of Demazure, Bott etc.). | |
| Jul 4, 2014 at 12:18 | comment | added | Matthias Wendt | @Sasha: I guess this is only the partial answer. There would also have to be a method to iteratively determine the first Chern class of the rank two bundle giving the $\mathbb{P}^1$-fibration. | |
| Jul 4, 2014 at 8:54 | comment | added | Sasha | These varieties are iterated $P^1$-fibrations. This can be used to compute the cohomology. | |
| Jul 4, 2014 at 5:19 | history | asked | Qiao | CC BY-SA 3.0 |