Common stabilizations of amalgamated Heegaard splitting and dual Heegaard splitting (Q2317442)

For a closed connected orientable $3$-manifold, the classical theorem by Reidemeister and Singer claims that any two Heegaard splittings will be equivalent after a finite number of stabilizations. The stable genus of the two splittings is defined to be the minimal genus of such a common stabilization.\par The main result of the present paper under review is to give an upper bound for the stable genus of an amalgamated Heegaard splitting and its dual Heegaard splitting in terms of genera of the Heegaard surfaces. Moreover, the upper bound is best possible. In fact, the upper bound is attained if a certain condition for Hempel distance is satisfied.