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On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds

Joel Hass·Shicheng Wang·Qing Zhou
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Abstract

For any hyperbolic 3-manifold $M$ with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of $\partial M$ or the volume of $M$ is bounded above. When the volume is bounded above, then area of $\partial M$ is bounded above and the length of closed geodesic on $\partial M$ is bounded below.

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Joel Hass, Shicheng Wang, Qing Zhou. 2000-02-01. On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds. https://arxiv.org/abs/math/0002002

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