$\partial$-reducible handle additions

Han Lou; Mingxing Zhang

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arXiv · 1810.09649

$\partial$-reducible handle additions

Han Lou·Mingxing Zhang

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Abstract

Let $M$ be a simple 3-manifold, and $F$ be a component of $\partial M$ of genus at least 2. Let $\alpha$ and $\beta$ be separating slopes on $F$. Let $M(\alpha)$ (resp. $M(\beta)$) be the manifold obtained by adding a 2-handle along $\alpha$ (resp. $\beta$). If $M(\alpha)$ and $M(\beta)$ are $\partial$-reducible, then the minimal geometric intersection number of $\alpha$ and $\beta$ is at most 8.

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Han Lou, Mingxing Zhang. 2018-10-23. $\partial$-reducible handle additions. https://arxiv.org/abs/1810.09649

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