Critical Heegaard Surfaces Obtained by Self-Amalgamation

Let M be a compact orientable irreducible 3-manifold and H be an unstabilized genus three Heegaard splitting of M . In this article, we will define a simplicial complex of weak reducing pairs for H and find several properties of this complex. Using this method, we will prove that an unstabilized Heegaard splitting of genus three is critical in a certain condition. In addition, we will show that the standard genus three Heegaard splitting for T 3 and the induced Heegaard splitting of the three component chain exterior by a certain tunnel system are critical as examples of the main theorem.

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Critical Heegaard Surfaces Obtained by Self-Amalgamation

Abstract: Abstract. Critical surfaces can be regarded as topological index 2 minimal surfaces which was introduced by David Bachman. In this paper we give a sufficiently condition and a necessary condition for selfamalgamated Heegaard surfaces to be critical.

Cited by 11 publications

References 11 publications

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

Unstabilized and uncritical self-amalgamation along essential subsurfaces

On unstabilized genus three critical Heegaard surfaces

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