Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori Dana Yon Phillips But the battles of tomorrow

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Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori Dana Yon Phillips But the battles of tomorrowWe show that if a hyperbolic knot manifold M contains an essential twicepunctured torus F with boundary slope ? and admits a filling with slope ? producing a Seifert fibred space, then the distance between the slopes ? and ? is less than or equal to 5 unless M is the exterior of the figure eight knot. The result is sharp; the bound of 5 can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the