On the equality between the Maslov index and the spectral index for the semi-Riemannian Jacobi operator (Q1604267)

The authors consider a Morse-Sturm system \(g^{-1}(gv')'=Rv\) where \(g(t)\) is a nondegenerate symmetric bilinear form on \(\mathbb{R}^n\), in the case where \(g\) is not necessarily positive definite. The main result of the paper is that two integer numbers naturally associated to the system: the Maslov index (defined in a topological framework) and the spectral index (defined in an analytic framework) are equal. In the case where \(g\) is not definite, the classical arguments fail due to the occurence of possible degeneracies. The authors use perturbation arguments to obtain the general case from the nondegenerating case. In particular, the authors prove the stability of the Maslov index and the spectral index as well as the genericity of the nondegeneracy conditions.