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

Hass, Joel; Wang, Shicheng; Zhou, Qing

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

Authors

Hass, Joel

Wang, Shicheng

Zhou, Qing

Description

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.
13 pages