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

Hass, Joel; Wang, Shicheng; Zhou, Qing

doi:10.1090/S0002-9939-01-06262-1

On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds
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by Joel Hass, Shicheng Wang and Qing Zhou PDF

Proc. Amer. Math. Soc. 130 (2002), 1851-1857 Request permission

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 $\partial M$ is bounded from above.

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