On Heegaard Splittings with Finitely Many Pairs of Disjoint Compression Disks
Received:July 27, 2022  Revised:October 05, 2022
Key Words: 3-manifolds   Heegaard splitting   weakly reducible   critical surfaces  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11671064).
Author NameAffiliation
Qiang E School of Science, Dalian Maritime University, Liaoning 116033, P. R. China 
Zhiyan ZHANG School of Science, Dalian Maritime University, Liaoning 116033, P. R. China 
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Abstract:
      Suppose $V\cup_S W$ is a genus-$g$ weakly reducible Heegaard splitting of a closed 3-manifold with finitely many pairs of disjoint compression disks on distinct sides up to isotopy 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 a unique separating compressing disk and $d(S_i)\geq 2$, for $i=1,2$. If there exist more than one but finitely many pairs of disjoint compression disks, at least one of $d(S_i)$ is 2 and $S$ is a critical Heegaard surface.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.04.012
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