Timeline for Understanding the odd-dimensional index
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2020 at 19:43 | comment | added | geometricK | @SebastianGoette Yes that is similar to the type of explanation I was looking for (although I'm not entirely sure yet what I should be looking for). | |
| Feb 29, 2020 at 8:03 | comment | added | Sebastian Goette | The odd index also comes up naturally in families: if the odd index of a fibrewise operator on odd-dimensional fibres is nonzero, the kernel cannot form a vector bundle over the base. Asobserved by Johannes Ebert, this is an old, but not so well-known fact. It has been exploited by Anja Wittmann in arXiv:1503.02002, see also the references there. | |
| Feb 29, 2020 at 7:57 | comment | added | Sebastian Goette | If $\dim M=8n+1$, the index of the real Dirac operator is given by the parity of $\dim\ker D$. Is that the kind of explanation you were hoping for? | |
| Feb 28, 2020 at 23:07 | comment | added | geometricK | Yes that is correct - I'm looking for an interpretation in the general case, including the closed case. | |
| Feb 28, 2020 at 23:05 | comment | added | Chris Gerig | To clarify, you are no longer asking about the Fredholm index of an elliptic (hence Fredholm) operator on a closed odd-dimensional manifold, but some other notion of an index. | |
| Feb 28, 2020 at 21:18 | history | edited | Denis Serre | CC BY-SA 4.0 |
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| Feb 28, 2020 at 21:10 | history | asked | geometricK | CC BY-SA 4.0 |