Timeline for Elliptic operators over noncompact manifold
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 1 at 22:06 | comment | added | Tom Mrowka | Let me add one more comment. The slogan for what is going on is that to get a Fredholm operator on a non-compact manifold you need "invertibility outside compact sets" for the operator on suitable spaces. Sometimes geometry can help for example the is Gromov and Lawson's paper [POSITIVE SCALAR CURVATURE AND THE DIRAC OPERATOR ON COMPLETE RIEMANNIAN MANIFOLDS]{ihes.fr/~gromov/wp-content/uploads/2018/08/840.pdf} where positive scalar curvature outside a compact set on a complete Riemannian manifold is enough to get a Fredholm Dirac operator. | |
| May 1 at 18:34 | comment | added | Tom Mrowka | Although I am a big fan of Lockhart and McOwens papers, many of the their results can easily be proved from the results of the paper of Atiyah, Patodi, Singer,Spectral Asymmetry and Riemannian Geometry. In particular Proposition 2.5 is a hairs breath away from the key result in the first order case. | |
| May 1 at 14:19 | vote | accept | TaiatLyu | ||
| May 1 at 13:42 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
deleted 9 characters in body
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| May 1 at 13:07 | history | answered | Igor Khavkine | CC BY-SA 4.0 |