This article is cited in 17 papers

The Index Locality Principle in Elliptic Theory

V. E. Nazaikinskii^a, B. Yu. Sternin<sup>b

a</sup> A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
^b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

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.

UDC: 517.9

Received: 21.01.2000

DOI: 10.4213/faa244

 English version: Functional Analysis and Its Applications, 2001, 35:2, 111–123

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