On Heegaard splittings with finite many pairs of disjoint compression disks

2022/06/15 by E Qiang, E, Qiang, Zhang Zhiyan +1
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2206.07415

Abstract

Suppose V∪_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∪_S W admits an untelescoping: (V₁∪_S1W₁)∪_F(W₂∪_S2V₂) such that W_i has only one separating compressing disk and d(S_i)≥ 2, for i=1,~2. If n>1, at least one of d(S_i) is 2 and S is a critical Heegaard surface.

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