Timeline for Atiyah-Singer index theorem
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2009 at 21:51 | comment | added | Spinorbundle | As far as I know the AS index theorem is an index theorem for elliptic differential operators, but several proofs use pseudodifferential operators. According to wikipedia: "Most version of the index theorem can be extended from elliptic differential operators to elliptic pseudodifferential operators." So perhaps you're right, but for more differential-geometric guys (like me) the most interesting cases are (generalized) Dirac operators. (My comment above is perhaps incorrect, but I had a kind of approximation in mind; perhaps something can point out wheter this is true or not) | |
| Dec 4, 2009 at 14:08 | comment | added | Andrea Ferretti | Isn't the general statement about elliptic pseudodifferential operators? As far as I know Dirac operators are elliptic differential operators, and even of a special kind. So I think I'm missing something very basic here; I always thought that the proof for Dirac operators was rather special. Pardon my ignorance, but I'm actually not of the field. | |
| Dec 4, 2009 at 13:36 | history | edited | Spinorbundle | CC BY-SA 2.5 |
Typos, formatting,...
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| Dec 4, 2009 at 13:27 | comment | added | Spinorbundle | Hmm, I think you're right. With "full" I meant AS for elliptic operators (in fact weak elliptic is enough). But it should be enough to proof the index theorem for (generalized) Dirac operators. | |
| Dec 4, 2009 at 7:03 | comment | added | José Figueroa-O'Farrill | But the general index theorem is the index theorem for some Dirac operator, so can't this be turned into a general proof? | |
| Dec 3, 2009 at 18:53 | history | edited | Spinorbundle | CC BY-SA 2.5 |
added 66 characters in body
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| Dec 3, 2009 at 18:26 | history | answered | Spinorbundle | CC BY-SA 2.5 |