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

Zhang, Mingxing; Qui, Ruifeng; Li, Yannan

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

Authors

Zhang, Mingxing

Qui, Ruifeng

Li, Yannan

Description

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.
17 pages, 26 figures