The distance between two separating, reducing slopes is at most 4

Mingxing Zhang; Ruifeng Qui; Yannan Li

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The distance between two separating, reducing slopes is at most 4

Mingxing Zhang·Ruifeng Qui·Yannan Li

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Abstract

Let $M$ be a simple 3-manifold such that one component of $\partial M$, say $F$, has genus at least two. For a slope $α$ on $F$, we denote by $M(α)$ the manifold obtained by attaching a 2-handle to $M$ along a regular neighborhood of $α$ on $F$. If $M(α)$ is reducible, then $α$ is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on $F$ is at most 4.

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BibTeX RIS

Mingxing Zhang, Ruifeng Qui, Yannan Li. 2006-09-29. The distance between two separating, reducing slopes is at most 4. https://arxiv.org/abs/math/0609830

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