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Boundary slopes of immersed surfaces in 3-manifolds

Boundary slopes of immersed surfaces in 3-manifolds

This paper presents some finiteness results for the number of boundary slopes of immersed proper 7ri-injective surfaces of given genus g in a compact 3-manifold with torus boundary.In the case of hyperbolic 3-manifolds we obtain uniform quadratic bounds in g, independent of the 3-manifold.