The additivity of the \(\eta\)-invariant. The case of a singular tangential operator (Q1894862)

Let \(M\) be a compact odd-dimensional Riemannian manifold without boundary, which is a sum of two submanifolds with common boundary. Let \(A: C^\infty(S)\to C^\infty(S)\) denote a Dirac operator acting on sections of a bundle of a Clifford module \(S\) over \(M\), \(\eta(A; s)\) denote the eta functions of \(A\), and \(\eta_A= \eta(A; 0)\) denotes the eta invariant of \(A\). The aim of this paper is to study the decomposition of \(\eta_A\) into the contributions coming from different parts of the manifold \(M\).