The Index Locality Principle in Elliptic Theory
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.
KeywordsFunctional Analysis Additional Condition Wide Class Elliptic Operator Symmetry Condition
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