Abstract
We prove a general theorem on the behavior of the relative index under surgery 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 some additional conditions (like symmetry conditions), this theorem permits computing 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.
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Nazaikinskii, V.E., Sternin, B.Y. The Index Locality Principle in Elliptic Theory. Functional Analysis and Its Applications 35, 111–123 (2001). https://doi.org/10.1023/A:1017527215489
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DOI: https://doi.org/10.1023/A:1017527215489