Mathematische Zeitschrift

, Volume 257, Issue 4, pp 799–810

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


DOI: 10.1007/s00209-007-0147-y

Cite this article as:
Zhang, M., Qiu, R. & Li, Y. Math. Z. (2007) 257: 799. doi:10.1007/s00209-007-0147-y


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.

Mathematics Subject Classification (2000)



S-cycleExtended S-cycleReducing slope

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsDalian University of TechnologyDalianPeople’s Republic of China