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Localization and surgery in the index theory of elliptic operators. (English. Russian original) Zbl 1054.58014
Dokl. Math. 61, No. 1, 13-16 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 370, No. 1, 19-23 (2000).
This paper proposes the notion of “bottleneck space” to encode the locality property of the index of elliptic operators. A bottleneck space is a Hilbert space endowed with a \(C^\infty([0,1])\)-module structure. In this setting the authors state a relative index formula. As an application, they state an index formula for cone operators under an assumption on the conormal symbol, called “Assumption A”. The same formula is claimed to be valid for Fourier-Maslov integral operators.

58J20 Index theory and related fixed-point theorems on manifolds
35J40 Boundary value problems for higher-order elliptic equations