The amalgamation of high distance Heegaard splittings along tori

Abstract

Let [Formula: see text] be a compact, connected, orientable closed 3-manifold. Let [Formula: see text] be a disjoint union of incompressible separating tori in [Formula: see text] which cut [Formula: see text] into the submanifolds [Formula: see text]. In the present paper, we show that the Heegaard genus [Formula: see text] of [Formula: see text] is given by [Formula: see text] provided that each [Formula: see text] has a Heegaard splitting [Formula: see text] with Hempel distance [Formula: see text].