On Heegaard splittings with finite many pairs of disjoint compression disks

Qiang E; Zhiyan Zhang

paper

On Heegaard splittings with finite many pairs of disjoint compression disks

arXiv:2206.07415

Abstract

Suppose $V \cup_{S} W$ is a weakly reducible Heegaard splitting of a closed 3-manifold which admits only $n$ pairs of disjoint compression disks on distinct sides and $g > 2$ . We show $V \cup_{S} W$ admits an untelescoping: $(V_{1} \cup_{S_{1}} W_{1}) \cup_{F} (W_{2} \cup_{S_{2}} V_{2})$ such that $W_{i}$ has only one separating compressing disk and $d (S_{i}) \geq 2$ , for $i = 1, 2$ . If $n > 1$ , at least one of $d (S_{i})$ is 2 and $S$ is a critical Heegaard surface.

arXiv admin note: text overlap with arXiv:1703.01718