Timeline for References for Stiefel-Whitney class of Stiefel manifolds and Grassmannians
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| S Apr 11, 2019 at 18:35 | history | suggested | user64494 | CC BY-SA 4.0 |
A typo is corrected.
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| Apr 11, 2019 at 17:34 | review | Suggested edits | |||
| S Apr 11, 2019 at 18:35 | |||||
| Mar 6, 2019 at 20:33 | answer | added | Michael Albanese | timeline score: 5 | |
| Oct 12, 2015 at 13:21 | comment | added | user43326 | @MarkGrant Actually I meant part I, chapter V. Of course, they dealt with only the case of $G_{n-1}(F^n)$, and depending on $F$, they calculate Chern and Pontryagin classes, but one should be able to deduce the Stiefel-Whitney classes from them (for example, by taking "square root" of Chern classes). | |
| Oct 12, 2015 at 13:17 | vote | accept | QSR | ||
| Oct 12, 2015 at 13:13 | answer | added | Mark Grant | timeline score: 9 | |
| Oct 12, 2015 at 12:54 | comment | added | Mark Grant | @user43326: In part III of the series of papers you mention they show that $w(G/S)=1$ where $G$ is a compact Lie group and $S$ is a toral subgroup. I couldn't see any other calculations of SW-classes of manifolds on a quick skim reading. | |
| Oct 12, 2015 at 9:58 | comment | added | user43326 | Aren't they in Borel-Hirzebruch, characteristic classes and homogeneous spaces? | |
| Oct 12, 2015 at 7:21 | comment | added | Mark Grant | To continue with the Wu formula you need to understand the mod 2 cohomology rings together with Poincaré duality and the action of the Steenrod algebra. This should certainly be tractable in your last 2 examples (and maybe your last 3, did you really mean to ask about the oriented Grassmannian there)? I agree this should be worked out somewhere. | |
| Oct 12, 2015 at 3:43 | comment | added | QSR | @RyanBudney Yes, Prof. Ryan. I found that $w$ is expressed in terms of $Sq$'s and Wu class $v$ [Th. 11.14]. However, I do not know how to continue... | |
| Oct 12, 2015 at 3:02 | review | Close votes | |||
| Oct 12, 2015 at 17:05 | |||||
| Oct 12, 2015 at 2:44 | comment | added | Ryan Budney | Have you looked in any of the standard characteristic classes references, such as Milnor and Stasheff? My impression is most of your questions are answered, or at least close to answered, there. | |
| Oct 12, 2015 at 1:06 | history | asked | QSR | CC BY-SA 3.0 |