Dehn surgery on complicated fibered knots in the 3-sphere

Abstract

Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K is sufficiently complicated, then Dehn surgery on K cannot yield a lens space. Work of Yi Ni shows that if K has a lens space surgery then it is fibered. Combining this with our result we see that if K has a lens space surgery then it is fibered and the monodromy is relatively simple.

References in corpus (2)

• Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs
• Monodromy action on unknotting tunnels in fiber surfaces

Cited by in corpus (1)

• Translation distance bounds for fibered 3-manifolds with boundary