Surgery and the relative index in elliptic theory
We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional condition...
| Main Authors: | , |
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| Format: | Others |
| Language: | English |
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Universität Potsdam
1999
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| Subjects: | |
| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25538 http://opus.kobv.de/ubp/volltexte/2008/2553/ |
| Summary: | We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol. |
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