Critical Heegaard surfaces obtained by amalgamation

Critical surfaces are defined by Bachman as topological index two surfaces, which are a natural extension of incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a special case, we obtain critical Heegaard surfaces by boundary stabilization. Also we give examples of unstabilized critical Heegaard surfaces—the standard Heegaard surfaces of (closed orientable surface)×S1.