Timeline for Characteristic classes of the bundle of trace free, skew adjoint endomorphisms
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2018 at 23:47 | vote | accept | Overflowian | ||
| Dec 3, 2018 at 20:58 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Dec 3, 2018 at 17:35 | comment | added | Overflowian | Thank you Igor. In my edition (2002) it is $-4c_2$ (pg. 146), but I agree with you that should be a $-2$. Can you recommend also some other references to undergo Donaldson book (apart from Milnor-Stasheff)? | |
| Dec 3, 2018 at 15:33 | comment | added | Igor Belegradek | Here is how these things usually go. One has to find a functorial relationship between a vector space $V$ and the vector space of trace-free, skew adjoint automorphisms of $V$. Then there is the same relationship between the corresponding vector bundles (see section 3 in Milnor-Stasheff). Finally there are standard relations between Chern, Stiefel-Whitney and Ponryagin classes (again, Milnor-Stasheff, exercise 14B and Corollary 15.5) which will probably imply the formulas in Donaldson's book. | |
| Dec 3, 2018 at 10:41 | history | asked | Overflowian | CC BY-SA 4.0 |