Timeline for Proving the basic identity which implies the Chern-Weil theorem
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2010 at 14:27 | vote | accept | Anirbit | ||
| Jun 23, 2010 at 15:01 | history | edited | Charles Matthews | CC BY-SA 2.5 |
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| Jun 23, 2010 at 12:32 | comment | added | skupers | These notes may help: staff.science.uu.nl/~ban00101/anman2009/lectures-10-11-12.pdf. They give a complete treatment of characteristic classes through the Chern-Weil point of view. | |
| Jun 23, 2010 at 10:50 | answer | added | Tom Boardman | timeline score: 3 | |
| Jun 22, 2010 at 23:01 | comment | added | bavajee | Sorry, please replace the second $C^{\infty}(M)$ with $C^{\infty}(M)$-linear in my posting above. | |
| Jun 22, 2010 at 23:00 | comment | added | bavajee | A connection is not a element of $\Omega^1(M,End(E))$, because it is not $C^{\infty}(M)$-linear. The difference of two connections is however $C^{\infty}(M)$. Therefore the set of connections is an affine space over $\Omega^1(M,End(E))$. | |
| Jun 22, 2010 at 22:41 | answer | added | bavajee | timeline score: 0 | |
| Jun 22, 2010 at 22:30 | answer | added | Willie Wong | timeline score: 2 | |
| Jun 22, 2010 at 20:36 | comment | added | Deane Yang | I meant a 1-dimensional complex vector bundle. It's the connection that is U(1). | |
| Jun 22, 2010 at 20:17 | comment | added | Anirbit | @Deane No. I at least got the impression that learning for vector bundles is easier first than for G-bundles. Anyway you have a good reference for that? @Steve Yes. Thats the Weiping's book I had in mind. | |
| Jun 22, 2010 at 19:50 | comment | added | Paul Siegel | I'll try to formulate a response to some of your specific questions if I have time later, but for now I'll just point you to the place where I learned this stuff: books.google.com/… Everything is worked out in great detail in chapters 17 and 18 (though the book only does the affine case). | |
| Jun 22, 2010 at 19:41 | answer | added | hce | timeline score: 1 | |
| Jun 22, 2010 at 19:36 | comment | added | Steve Huntsman | Are you working from this book? books.google.com/books?id=T08AwbrdEPcC | |
| Jun 22, 2010 at 19:35 | comment | added | Deane Yang | Have you worked out the details for a U(1) connection on a complex line bundle? This case is easier but instructive. It is worth doing first. | |
| Jun 22, 2010 at 19:15 | history | asked | Anirbit | CC BY-SA 2.5 |