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

@inproceedings{Zhang2006TheDB,
title={The distance between two separating , reducing slopes is at most 4},
author={Mingxing Zhang and Ruifeng Qiu and Yannan Li},
year={2006}
}

Let M be a simple 3-manifold such that one component of ∂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.