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Surgery and the relative index in elliptic theory. (English) Zbl 1133.58014
Summary: This is a survey article featuring the general index locality principle introduced by the authors, which can be used to obtain index formulas for elliptic operators and Fourier integral operators in various situations, including operators on stratified manifolds and manifolds with singularities.

58J20 Index theory and related fixed-point theorems on manifolds
35J45 Systems of elliptic equations, general (MSC2000)
47G30 Pseudodifferential operators
58J30 Spectral flows
58J40 Pseudodifferential and Fourier integral operators on manifolds
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