Boundary slopes of immersed surfaces in 3-manifolds

Details Boundary slopes of immersed surfaces in 3-manifolds Boundary slopes of immersed surfaces in 3-manifolds

1999-11-10

arxiv.org/abs/math/9911072v1

Mathematics

Geometric Topology

Scientific paper

This paper presents some finiteness results for the number of boundary slopes of immersed essential 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 for the number of possible slopes, independent of the 3-manifold. We also look at some related quantities, such as how many times the slopes of two such surfaces of specified genus can intersect.

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