Localization and surgery in the index theory of elliptic operators. (Q1432159)

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.