Geometriae Dedicata

, Volume 147, Issue 1, pp 131–138 | Cite as

A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

  • Tao Li
  • Ruifeng Qiu
  • Shicheng Wang
Original Paper


Let M be an orientable 3-manifold with ∂M a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most g is bounded by a quadratic function of g. In the hyperbolic case, this was proved earlier by Hass et al.


Boundary slope Essential surface 

Mathematics Subject Classification (2000)

57M50 57N10 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiChina
  3. 3.Department of MathematicsPeking UniversityBeijingChina

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