2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99789Given a 3-manifold M containing an incompressible surface Q, we obtain an inequality relating the Heegaard genus of M and the Heegaard genera of the components of M - Q. Here the sum of the genera of the components of M - Q is bounded above by a linear expression in terms of the genus of M, the Euler characteristic of Q and the number of parallelism classes of essential annuli for which representatives can be simultaneously imbedded in the components of M - Q.21 pages, 17 figuresGeometric Topology57N10text