Critical Heegaard surfaces obtained by amalgamation

Abstract

Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing 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. It gives critical Heegaard surfaces of non-minimal genus, for 3-manifolds which do not admit distinct Heegaard splittings (up to isotopy).

7 pages, 3 figures

References in corpus (1)

• Examples of unstabilized critical Heegaard surfaces

Cited by in corpus (1)

• Mapping class groups of Heegaard splittings of surface bundles