2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71184We describe a relation between Atiyah-Patodi-Singer boundary condition and a global elliptic boundary condition which naturally appears in formulating a splitting formula for a spectral flow, when we decompose the manifold into two components. Then we give a variant of the splitting formula with the Hoermander index as a correction term.10 pages, no figureSymplectic GeometryDifferential Geometry53D12;58J30;58J32text