Timeline for Can one use Atiyah-Singer to prove that the Chern-Weil definition of Chern classes are $\mathbb{Z}$-cohomology classes?
Current License: CC BY-SA 3.0
4 events
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| Jul 11, 2011 at 15:38 | comment | added | Aaron Mazel-Gee | Thank you. This was my original intuition, that the hypotheses of the index theorem seem too specialized to give this general result about Chern classes. | |
| Jun 30, 2011 at 16:02 | comment | added | Johannes Ebert | The bundle you twist with comes in via the Chern character, which is additive. This can be used to show the integrality of the Chern character on spehres, for example. But the (total) Chern class is not additive. | |
| Jun 30, 2011 at 13:32 | comment | added | Paul Siegel | The index theorem is a little more flexible than this - you can always twist your operator by a coefficient bundle, for example. But I agree that it is not flexible enough for Chern-Weil theory. | |
| Jun 29, 2011 at 8:35 | history | answered | Johannes Ebert | CC BY-SA 3.0 |