AN EXAMPLE OF A HYPERBOLIC 3-MANIFOLD REALIZING A BOUND ON DEHN FILLINGS

Let M be a compact, orientable, irreducible 3-manifold with an incompressible torus boundary T and γ a longitudinal slope on T, which bounds a surface F of genus 2. Suppose there exists a slope r that produces an essential 2-sphere S by Dehn filling. Let q be the minimal geometric intersection number between the essential 2-sphere and the core of the Dehn filling. Matignon and Sayari [5] proved that either q = 2 or the minimal geometric intersection number between γ and r is bounded by 3. Here, we construct an example of a hyperbolic 3-manifold realizing that bound.