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

Tao Li; Ruifeng Qiu; Shicheng Wang

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arXiv · 0905.1499

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

Tao Li·Ruifeng Qiu·Shicheng Wang

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Abstract

Let $M$ be an orientable 3-manifold with $\partial M$ 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, Rubinstein and Wang.

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Tao Li, Ruifeng Qiu, Shicheng Wang. 2009-06-12. A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus. https://arxiv.org/abs/0905.1499

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