Timeline for Chern-Weil theory and Weil homomorphism of principal bundle
Current License: CC BY-SA 4.0
11 events
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| Nov 2, 2019 at 13:20 | comment | added | Praphulla Koushik | @PanagiotisKonstantis ok... That helps :) I will think and ask if I have any further question... | |
| Nov 2, 2019 at 13:05 | comment | added | Panagiotis Konstantis | @PraphullaKoushik E.g. if a Chern class is a torsion element in $H^k(M;\mathbb Z)$ then it has to be mapped to zero under the homomorphism $H^k(M;\mathbb Z) \to H^k(M;\mathbb R)$ since the latter group do not contain torsion. But with C-W theory you construct exactly this zero class in $H^k(M;\mathbb R)$ (where $H^k(M;\mathbb R)$ is understood to be the deRham cohomology) | |
| Nov 2, 2019 at 12:44 | comment | added | Praphulla Koushik | @PanagiotisKonstantis Is that so, I did not observe it.. can you kindly explain why it does not see torsion? Any reference would be helpful.. Thanks for the comment :) | |
| Nov 2, 2019 at 11:26 | comment | added | Panagiotis Konstantis | This is a comment in addition to David's comment. If you want to define Chern classes via C-W-theory you "only" get the images of the Chern classes defined in Milnor's book under the coefficient homomorphism $H^k(M;\mathbb Z) \to H^k(M;\mathbb R)$. In particular C-W cannot see torsion phenomena. | |
| Nov 2, 2019 at 8:59 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Nov 2, 2019 at 8:07 | comment | added | Praphulla Koushik | @DavidRoberts I mean characteristic classes are also defined using connection and for this Chern-Weil homomorphism is used... I am not 100% sure if this also is grammatically correct :) please feel free to edit to make it look correct... | |
| Nov 2, 2019 at 7:26 | comment | added | David Roberts♦ | Characteristic classes are not defined via Chern–Weil theory, rather the C–W theory gives another way to construct them. If you haven't seen it, the classic Characteristic classes by Milnor and Stasheff is worth checking out. | |
| Nov 2, 2019 at 6:16 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Oct 3, 2019 at 4:32 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Mar 23, 2019 at 7:39 | history | edited | Praphulla Koushik |
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| Mar 13, 2019 at 1:24 | history | asked | Praphulla Koushik | CC BY-SA 4.0 |